Method and apparatus for self-referenced dynamic step and scan intra-field scanning distortion

ABSTRACT

Techniques for determining wafer stage grid and yaw in a projection imaging tool are described. The techniques include exposing an overlay reticle onto a substrate having a recording media, thereby creating a plurality of printed fields on the substrate. The overlay reticle is then positioned such that when the reticle is exposed again completed alignment attributes are created in at least two sites in a first and a second printed field. The substrate is then rotated relative to the reticle by a desired amount. The overlay reticle is then positioned such that when the reticle is again exposed, completed alignment attributes are created in at least two sites in the first and a third printed field. Measurements of the complementary alignment attribute and a dynamic intra-field lens distortion are then used to reconstruct wafer stage grid and yaw error of the projection imaging system.

REFERENCE TO PRIORITY DOCUMENT

This application is a continuation-in-part, and claims the benefit ofpriority, of co-ending U.S. patent application Ser. No. 11/102,382entitled “Method and Apparatus for Self-Referenced Dynamic Step and ScanIntra-Field Scanning Distortion”, filed Apr. 8, 2005 and co-pending U.S.patent application Ser. No. 10/252,021, entitled “Method and Apparatusfor Self-Referenced Dynamic Step and Scan Intra-Field ScanningDistortion”, filed Sep. 20, 2002, which claimed the benefit of priorityof U.S. Provisional Patent Application Ser. No. 60/323,577, entitled“Method for Self-Referenced Dynamic Step and Scan Intra-Field ScanningDistortion”, filed Sep. 20, 2001. Priority of the filing date of Sep.20, 2001 is hereby claimed, and the disclosures of U.S. patentapplication Ser. No. 11/102,382, U.S. patent application Ser. No.10/252,021, and U.S. Provisional Patent Application Ser. No. 60/323,577are hereby incorporated in their entirety by reference.

BACKGROUND

1. Field of the Invention

The present invention relates generally to processes for semiconductormanufacturing and more particularly to characterizing and monitoring theintra-field distortions of scanning projection systems used in ULSIphotolithography.

2. Description of the Related Art

Today's lithographic processing requires ever tighter layer-to-layeroverlay tolerances to meet device performance requirements. Overlayregistration on critical layers can directly impact device performance,yield and repeatability. Typical microelectronic devices or circuits mayhave as many as 20 or more levels or pattern layers. The placement ofpatterned features on one level must match the placement ofcorresponding features on other levels—that is, they must overlap—withinan accuracy which is some fraction of the minimum feature size orcritical dimension (CD).

Overlay error is typically, although not exclusively, measured with ametrology tool appropriately called an overlay tool using severaltechniques. See Semiconductor Pattern Overlay, N. Sullivan, SPIECritical Reviews Vol. CR52, 160:188. The term overlay metrology tool oroverlay tool means any tool capable of determining the relative positionof two alignment attributes that are separated within about 2000 um(microns) of each other. The importance of overlay error, and its impacton yield, have been extensively studied and documented. See MeasuringFab Overlay Programs, R. Martin et al., SPIE Conference on Metrology,Inspection, and Process Control for Microlithography XIII, 64:71, March1999;

-   -   A New Approach to Correlating Overlay and Yield, M. Preil et        al., SPIE Conference on Metrology, Inspection, and Process        Control for Microlithography XIII, 208:216, March 1999.

Lithographers have created statistical computer algorithms (for example,Klass II (See Lens Matching and Distortion Testing in a Multi-Stepper,Sub-Micron Environment, A. Yost et al., SPIE Vol. 1087, 233:244, 1989)and Monolith (See A Computer Aided Engineering Workstation forRegistration Control, E. McFadden et al., SPIE Vol. 1087, 255:266,1989)) that attempt to quantify and divide overlay error into repeatableor systematic and non-repeatable or random effects. See Matching ofMultiple Wafer Steppers for 0.35 Micron Lithography Using AdvancedOptimization Schemes, M. van den Brink et al., SPIE Vol. 1926, 188:207,1993; A Computer Aided Engineering Workstation for Registration Control,supra; Semiconductor Pattern Overlay, supra; Machine Models andRegistration, T. Zavecz, SPIE Critical Reviews Vol. CR52, 134:159. Anoverall theoretical review of overlay modeling can be found in theliterature. See Semiconductor Pattern Overlay, supra.

Overlay error is typically divided into the following two majorcategories. The first category, inter-field or grid overlay error, isconcerned with the actual position of the translation and rotation oryaw of the image field as recorded in the photoresist on a silicon waferusing an exposure tool, i.e., stepper or scanner. The second category,intra-field overlay error, is the positional offset of an individualpoint inside a field referenced to the nominal center of an individualexposure field. Intra-field overlay errors are generally composed oflens aberrations or distortions, scanning irregularities, and reticlealignment.

It is important for this discussion to realize that most overlaymeasurements are made on silicon product wafers after eachphotolithographic process, prior to final etch. Product wafers cannot beetched until the photoresist target patterns are properly aligned to theunderlying target patterns. See Super Sparse Overlay Sampling Plans: AnEvaluation of Methods and Algorithms for Optimizing Overlay QualityControl and Metrology Tool Throughput, J. Pellegrini, SPIE Vol. 3677,72:82. Manufacturing facilities rely heavily on exposure tool alignmentand calibration procedures to help insure that the scanner tools arealigning properly. See Stepper Matching for Optimum Line Performance, T.Dooly et al., SPIE Vol. 3051, 426:432, 1997; Mix-and-Match: A NecessaryChoice, R. DeJule, Semiconductor International, 66:76, February 2000;Matching Performance for Multiple Wafer Steppers Using an AdvancedMetrology Procedure, M. Van den Brink, et al., SPIE Vol. 921, 180:197,1988. Inaccurate overlay modeling algorithms can corrupt the exposuretool calibration procedures and degrade the alignment accuracy of theexposure tool system. See Super Sparse Overlay Sampling Plans: AnEvaluation of Methods and Algorithms for Optimizing Overlay QualityControl and Metrology Tool Throughput, supra.

Over the past 30 years the microelectronics industry has experienceddramatic rapid decreases in critical dimension by constantly improvingphotolithographic imaging systems. Today, these photolithographicsystems are pushed to performance limits. As the critical dimensions ofsemiconductor devices approach 50 nm the overlay error requirements willsoon approach atomic dimensions. See Life Beyond Mix-and-Match:Controlling Sub-0.18 Micron Overlay Errors, T. Zavecz, SemiconductorInternational, July 2000. To meet the needs of next generation devicespecifications new overlay methodologies will need to be developed. Inparticular, overlay methodologies that can accurately separate outsystematic and random effects and break them into assignable causes willgreatly improve device process yields. See A New Approach to CorrelatingOverlay and Yield, supra. In particular, those new overlay methodologiesthat can be implemented into advanced process control or automatedcontrol loops will be most important. See Comparisons of Six DifferentIntra-Field Control Paradigms in an Advanced Mix and Match Environment,J. Pellegrini, SPIE Vol. 3050, 398:406, 1997; Characterizing OverlayRegistration of Concentric 5× and 1×Stepper Exposure Fields UsingInter-Field Data, F. Goodwin et al., SPIE Vol. 3050, 407:417, 1997.Finally, another area where quantifying lens distortion error is ofvital concern is in the production of photo masks or reticles during theelectron beam manufacturing process. See Handbook of Microlithographyand Microfabrication, P. Rai-Choudhury, Vol. 1, 417 1997.

Semiconductor manufacturing facilities use some version of the followingcomplex overlay procedure to help determine the magnitude of intra-fielddistortion independent of other sources of systematic overlay error—infact, the technique is used for both photolithographic steppers andscanners. The technique has been simplified for illustration. SeeAnalysis of Image Field Placement Deviations of a 5× MicrolithographicReduction Lens, D. MacMillen et al., SPIE Vol. 334, 78:89, 1982. FIG. 33shows a typical overlay target—one large or outer box and one small orinner target box. FIG. 31 shows a typical portion of a distortion testreticle used in the prior art. It should be noted that the chrome targetpatterns on most reticles are 4 or 5 times larger as compared with thepatterns they produce at the image plane, this simply means modern stepand scan systems (scanners) are reduction imaging systems. Further, forpurposes of discussion, it is assumed that the reticle pattern isgeometrically perfect, (in practice, the absolute positions of featureson the reticle can be measured and the resulting errors subtracted off).First, a wafer covered with photoresist is loaded onto the wafer stageand globally aligned. Next, the full-field image of the reticle, seeFIG. 2, is exposed onto the photoresist-coated wafer. See FIGS. 31 and32. For purposes of illustration, it is assumed that the distortion testreticle consists of a 5×5 array of outer boxes evenly spaced a distanceM*P, across the reticle surface, see FIG. 2. It is typically assumedthat the center of the optical system is virtually aberration free. SeeAnalysis of Image Field Placement Deviations of a 5× MicrolithographicReduction Lens, supra. With this assumption, the reticle, shown in FIG.2 is now partially covered using the virtual reticle blades, as shown inFIG. 18, in such a way that only a single target at the center of thereticle field, box A in FIG. 2, is available for exposure. Next, thewafer stage is moved in such a way as to align the center of the reticlepattern directly over the upper left hand corner of the printed 5×5outer box array, wafer position 1 in FIG. 31. The scanner then exposesthe image of the small target box onto the photoresist coated wafer. Ifthe wafer stage, optical system and scanning dynamics were truly perfectthen the image of the small target box would fit perfectly inside theimage of the larger target box, see FIG. 33, from the previous exposure.At this point the scanner and wafer stage are programmed to step andexpose the small target box in the 5×5 array where each exposure isseparated from the previous one by the stepping distance P.

With the assumption of a perfect stage, the final coordinates of thesmall target boxes are assumed to form a perfect grid, where the spacingof the grid is equal to the programmed stepping distance, P. Finally, ifthe first full-field exposure truly formed a perfect image, then theentire 5×5 array of smaller target boxes would fit perfectly inside the5×5 array of larger target boxes. Since the first full-field exposurepattern is in fact distorted due to an imperfect imaging system (andscanner system) the actual position of the larger target box will bedisplaced relative to the smaller target boxes. The wafer is then sentthrough the final few steps of the lithographic process to create thefinal photoresist patterned overlay targets.

The resulting overlay error at each field position can be measured witha standard optical overlay tool and the result is interpreted as beingintra-field error. Using the models described below in Equations 1 and2, the overlay data can be analyzed and the lens distortion error iscalculated.

The following intra-field modeling equations are commonly used to fitthe overlay data using a least square regression technique. See Analysisof Image Field Placement Deviations of a 5× Microlithographic ReductionLens, supra; Super Sparse Overlay Sampling Plans: An Evaluation ofMethods and Algorithms for Optimizing Overlay Quality Control andMetrology Tool Throughput, supra.dxf(xf,yf)=Tx+s*xf−q*yf+t1*xf2+t2*xf*yf−E*(xf ³ +xf*yf ²)  Equation 1dyf(xf,yf)=Ty+s*yf+q*xf+t2*yf ² +t1*xf*yf−E*(yf ³ +yf*xf ²)  Equation 2where;

-   (xf,yf)=intra-field coordinates-   (dxf, dyf)(xf,yf)=intra-field distortion at position (xf,yf)-   (Tx, Ty)=(x,y) intra-field translation-   s=intra-field overall scale or magnification-   q=intra-field rotation-   (t1, t2)=intra-field trapezoid error-   E=intra-field lens distortion.

A problem with this technique is two-fold, first, it is standardpractice to assume that the wafer stage error is very small, randomlydistributed, and can be completely accounted for using a statisticalmodel. See Analysis of Image Field Placement Deviations of a 5×Microlithographic Reduction Lens, supra; A “Golden Standard” WaferDesign for Optical Stepper Characterization”, K. Kenp et al., SPIE Vol.1464, 260:266, 1991; Matching Management of Multiple Wafer SteppersUsing a Stable Standard and a Matching Simulator, M. Van den Brink etal., SPIE Vol. 1087, 218:232, 1989; Matching Performance for MultipleWafer Steppers Using an Advanced Metrology Procedure, supra. In general,positional uncertainties in the wafer stage introduces both systematicand random errors, and since the intra-field distortion is measured onlyin reference to the lithography tool's wafer stage, machine to machinewafer stage differences show up as inaccurate intra-field distortionmaps. Secondly, the assumption that lens distortion is zero at thecenter of the lens is incorrect. Furthermore, the model represented byEquations 1 and 2 is entirely unsuited to modeling scanner overlayerror—typically the intra-field distortion model accounts only forscanner skew and scanner scale overlay errors—in general, thesynchronization errors between the reticle stage and wafer stageintroduce more complex errors described below.

A technique for stage and ‘artifact’ self-calibration is described inSee Self-Calibration in two-Dimensions: The Experiment, M. Takac et al.,SPIE Vol. 2725, 130:146, 1996; Error Estimation for Lattice Methods ofStage Self-Calibration, M. Raugh, SPIE Vol. 3050, 614:625, 1997. Itconsists of placing a plate (artifact) with a rectangular array ofmeasurable targets on a stage and measuring the absolute positions ofthe targets using a tool stage and the tool's image acquisition oralignment system. This measurement process is repeated by reinsertingthe artifact on the stage but shifted by one target spacing in theX-direction, then repeated again with the artifact inserted on the stageshifted by one target spacing in the Y-direction. Finally, the artifactis inserted at 90-degrees relative to its initial orientation and thetarget positions measured. The resulting tool measurements are a set of(x, y) absolute positions in the tool's nominal coordinate system. Then,the absolute positions of both targets on the artifact and a mixture ofthe repeatable and non-repeatable parts of the stage x, y grid error arethen determined to within a global translation (Txg, Tyg), rotation (qg)and overall scale ((sxg+syg)/2) factor.

This technique has several drawbacks, including that it requires thatthe measurements be performed on the same machine that is being assessedby this technique.

Furthermore, this technique requires measurements made on a tool inabsolute coordinates; the metrology tool measures the absolute positionof the printed targets relative to its own nominal center; so absolutemeasurements are required over the entire imaging field, with a typicalsize greater than about 100 mm²).

Another technique for the determination of intra-field distortion is themethod of Smith, McArthur, and Hunter (“Method And Apparatus ForSelf-Referenced Projection Lens Distortion Mapping”, U.S. patentapplication Ser. No. 09/835,201, now U.S. Pat. No. 6,573,986). It is aself-referencing technique that can be utilized with overlay metrologytools in a production environment. For diagnosing the intra-fieldscanner distortion in the presence of significant scannernon-repeatability, this technique teaches the use of a special reticlethat has reduced optical transmission that is multiply scanned producingsub-Eo exposures on the wafer. The result is that this technique can beused to accurately determine the repeatable part of the scannerintra-field distortion but not that part of the intra-field distortionthat changes from scan to scan, a simple example of which is the scannery-magnification.

Another drawback to these techniques to determine intra-field error isthat they use the scanner itself as the metrology tool. Due to the costof scanners, which can exceed 10 million dollars, it is desirable tohave a technique for intra-field error that does not use the scanneritself as the metrology tool for determining intra-field distortion bututilizes relatively inexpensive overlay metrology tools. Furthermore, itis desirable that the technique be easy to perform thereby allowing itto be used in a production environment by the day-to-day operatingpersonnel. It is further desirable to have a technique that measures thenon-repeatable parts of the scanner intra-field distortion.

Therefore there is a need for an effective, and efficient, way todetermine the scanner intra-field error.

SUMMARY

In accordance with the invention, techniques for determining wafer stagegrid and yaw in a projection imaging tool are described. The techniquesinclude exposing an overlay reticle in at least three positions onto asubstrate having a recording media. This exposure creates a plurality ofprinted fields on the substrate. The overlay reticle is then positionedsuch that, when the reticle is exposed again, completed alignmentattributes are created in at least two sites in first and second printedfields. The substrate is then rotated relative to the reticle by adesired amount. The overlay reticle is then positioned such that whenthe reticle is again exposed, completed alignment attributes are createdin at least two sites in the first printed field and in a third printedfield. Measurements of the complementary alignment attribute and adynamic intra-field lens distortion are then used to reconstruct waferstage grid and yaw error of the projection imaging system.

Rotating the substrate a desired amount can include rotating 90 degrees.Also, the measurements of the complementary alignment attribute can bemade with an overlay metrology tool. Different types of substrates caninclude a semiconductor wafer, a flat panel display, a reticle, or anelectronic recording media. Different types of projection imagingsystems can include a photolithograph step and scan machine, aphotolithographic scanner machine, a scanning electron beam imagingsystem, a scanning direct write tool, a scalpel tool, a scanning extremeultra-violet photolithographic tool, or a scanning x-ray imaging system.In addition, the recording media can include a positive photoresistmaterial, a negative photoresist material, an electronic CCD, a diodearray, a liquid crystal, or an optically sensitive material.

Determining wafer stage grid and yaw in a projection imaging tool canalso include exposing an overlay reticle in at least four positions ontoa substrate having a recording media, thereby creating a plurality ofprinted fields, then positioning the overlay reticle such that, when thereticle is exposed again, completed alignment attributes are created inat least two sites in first and second printed fields. The overlayreticle is then positioned such that when the reticle is exposed again,completed alignment attributes are created in at least two additionalsites in third and fourth printed fields. The substrate is then rotated90 degrees and the overlay reticle positioned such that, when thereticle is exposed, completed alignment attributes are created in atleast two sites in the first and third printed fields. Again, theoverlay reticle is positioned such that when the reticle is now exposedcompleted alignment attributes are created in at least two sites in thesecond and fourth printed fields. Measurements of the complementaryalignment attribute and a dynamic intra-field lens distortion are usedto reconstruct wafer stage grid and yaw error of the projection imagingsystem.

The operation of the projection imaging system can be adjusted inresponse to the reconstructed wafer grid and yaw error. For example, acontroller in the projection imaging system can adjust the operation ofthe imaging system in response to the reconstructed wafer grid and yawerror. The positioning of the reticle relative to the substrate can beaccomplished by a translation stage such as a wafer stage or a reticlestage or both. Likewise the substrate can be rotated relative to thewafer by a rotational stage, such as a wafer stage, reticle stage, orboth.

The techniques can be used to improve semiconductor fabrication thatuses a photolithographic projection tool. For example, operation of theprojection imaging system can be adjusted in response to thereconstructed wafer grid and yaw error to improve throughput, or yield,in a semiconductor fabrication process.

Other features and advantages of the present invention should beapparent from the following description of the preferred embodiment,which illustrates, by way of example, principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a scanner exposure field, scanner slit and scannercoordinate system.

FIG. 2 schematizes a reticle used for stage metered scan and lensdistortion.

FIG. 3 shows typical overlay patterns or completed alignment attributes.

FIG. 4 shows vector plots or lens distortion error in the absence ofscanner synchronization error.

FIG. 5 shows the components making up the instantaneous scanningsynchronization error.

FIG. 6 is a schematic of the reticle for the preferred embodiment forextracting dynamic intra-field scanning error.

FIG. 7 is an exemplary overlay group, OG, for a dark field mask withdimensions in microns.

FIG. 8 is a completed alignment attribute using AA and AA′ of FIG. 7.

FIG. 9 shows on the left exemplary overlay group OG for a bright fieldmask and on the right overlay group OG as projected onto the wafer at4:1 reduction.

FIG. 10 shows a completed alignment attribute using AA and AA′ of FIG. 9as printed in positive photoresist.

FIG. 11 is a side view of the reticle of FIG. 6.

FIG. 12 shows the process flow for the preferred embodiment of thisinvention.

FIG. 13 shows a second embodiment of the preferred reticle.

FIG. 14 shows a data file that represents the final results of themethod of this invention.

FIG. 15 shows an exposure plan for determining dynamic scan error offield F.

FIG. 16 shows a wafer with wafer alignment marks suitable for using thewafer at 0 and 90 degree orientations.

FIG. 17 shows a wafer after the first exposure for determining thedynamic scan distortion.

FIG. 18 shows a wafer after exposures done at 0 degrees and 90 degrees.

FIG. 19 shows the intrafield coordinate convention.

FIG. 20 shows schematics used in FIG. 18.

FIG. 21 shows an example of a minimal overlay group as realized on adark field reticle for carrying out the method of this invention.

FIG. 22 shows overlapped overlay groups OLAP1, OLAP2, OLAP3 as realizedwith the overlay group of FIG. 21.

FIG. 23 shows an overlay group OG consisting of a pair of waferalignment marks.

FIG. 24 shows overlapped overlay groups OLAP1, OLAP2, OLPA3 as realizedwith the overlay group of FIG. 23.

FIG. 25 shows an exemplary overlay group consisting of a single waferalignment mark.

FIG. 26 shows overlapped overlay groups OLAP1, OLAP2, OLAP3 as realizedwith the overlay group of FIG. 25.

FIG. 27 shows the wafer coordinate systems used in the discussion ofthis invention.

FIG. 28 shows in cross section a partially transmitting variation of thepresent invention that utilizes a partially reflecting surface as thetransmission reduction mechanism.

FIG. 29 shows in cross section a partially transmitting variation of thepresent invention that utilizes an attenuated phased shift mask on thesurface as the transmission reduction mechanism.

FIG. 30 shows in cross section another variation of the presentinvention that utilizes a reflective reticle.

FIG. 31 shows an example of a prior art lens distortion test exposurepattern.

FIG. 32 explains the schematics used in FIG. 2.

FIG. 33 shows a perfectly overlaid box in box structure.

FIG. 34 shows OLAP1, OLAP2, and OLAP3 as realized with overlay group ofFIG. 7.

FIG. 35 is a flow chart illustrating a technique for measurement ofwafer stage grid and yaw errors when operating in dynamic mode.

FIG. 36 is a schematic illustrating a wafer with wafer alignment markssuitable for alignment at two notch angles offset by 90 degrees fromeach other.

FIG. 37 is a plan view of a portion of a reticle illustrating sets ofoverlay groups (OLG).

FIG. 38 is a schematic illustrating further details of an overlayalignment group.

FIG. 39 is a plan view of a completed alignment attribute.

FIG. 40 is a schematic illustrating a wafer after exposure of an overlayreticle according to modified production plan layout.

FIG. 41 is a schematic illustrating a wafer after exposure of horizontalcross ties.

FIG. 42 is a schematic illustrating further detail of a horizontal crossrow.

FIG. 43 is a schematic illustrating a wafer after exposure of verticalcross ties.

FIG. 44 is a schematic illustrating a layout of horizontal cross rows(HCR) and vertical cross columns (VCC) on a wafer.

FIG. 45 is a schematic illustrating indices for a vertical cross columnused to describe an exemplary technique used to make overlaymeasurements.

FIG. 46 is a table illustrating an exemplary output listing of stagegrid and yaw errors for a scanner operating in dynamic mode.

FIG. 47 is a block diagram of an example of a projection imaging tool.

DETAILED DESCRIPTION

An aspect of the invention is that it does not require that measurementsbe made on the same machine that is being assessed accordinglydetermining the intra-field lens distortion can, and preferably are,made on an overlay metrology tool quite distinct from the projectionlithography tool that we are assessing.

Another aspect of the invention is that the absolute position of theprinted targets relative to the nominal center of the metrology tool isnot required, instead relative coordinates or displacements of features(box in box structures or some other alignment attribute) are measuredwith respect to each other. Because the distances between thesealignment attributes is typically less than 2.0 mm absolute position isnot required. In the case of box in box structures these distances aretypically less than about 0.2 mm. This difference is a significant onesince absolute metrology tools such as the Leica LMS 2000, Leica IPRO(See Leica LMS IPRO Brochure), or Nikon 5I (See Measuring System XY-5i,K. Kodama et al., SPIE Vol. 2439, 144:155, 1995) typically cost inexcess of 2 million dollars and are uncommon in semiconductormanufacturing facilities (fabs) while overlay metrology tools such asthe KLA 5200, or Bio-rad Q7 typically cost about half a million dollarsor more and are widely deployed in fabs. Another drawback of thistechnique is that it requires that the intra-field distortion berepeatable from exposure to exposure, this is precluded by the scannerdynamics.

Another aspect of the invention is that it utilizes a procedure thatgreatly reduces the number of measurements required to determine theintra-field lens distortion. Furthermore, the technique allows for thedetermination of the non-repeatable part of the scanner dynamicdistortion.

The structure of scanner intra-field distortion or translational errorcan be decomposed into a lens component, dependent only on theprojection imaging objective or projection system aberrations (See FIG.4), and a scanning component, dependent only on the relative dynamics ofthe wafer and reticle scanning motion. (See FIG. 5.) The lens componentis repeatable but the scanning component contains both repeatable andnon-repeatable parts. Furthermore, the lens and scanning components havecertain functional forms that simplify the extraction of intra-fielderror. A photolithographic step and scan or scanner system produces animage, typically reduced 4× or 5×, of the reticle pattern in the surfaceof the photoresist by continuously passing exposure radiation through asmall portion of the projection optics as the reticle and wafer stagetravel in opposite directions, as shown in FIG. 18. The scanning reticlestage and scanning wafer stage move in opposite directions in acoordinated manner at two different speeds.

FIG. 1 shows an instantaneous (top down) view of a partially exposedscanner field (and coordinate system) as it might appear on aphotoresist coated silicon wafer during a scan. Lack of coordinationbetween the wafer stage and reticle stage in the absence of lensdistortion will manifest itself as translational offseterror—ΔT(x,y,ys). Where ΔT(x,y,ys) is defined to be the instantaneoustranslational offset error on the wafer at intra-field positionx,y—located inside the image of the lens slit—when the scanner is atposition (ys), See FIG. 1. The final distortion error or overlay error(ΔF(x,y) at any point actually imaged in the photoresist is then anaverage of the instantaneous errors (ΔT(x,y,ys), weighted by theintensity function of the scanning slit. If the scanner operatedperfectly (without synchronization or vibration errors) then the finaldistortion or translational error, ΔsL(x) at each field point in thephotoresist would simply be the average of the static projection lensdistortion Δd(x) weighted by the intensity function of a static scannerslit. See aberration averaging; Performance of a Step and Scan Systemfor DUV Lithography, G. de Zwart et al., SPIE Vol. 3051, 817:835, 1997.

Thus, there are two independent sources of transverse scanning error orscanning distortion; projection lens distortion error—that varies inmagnitude and direction across the scanner field (in the x direction, orperpendicular to the scanning direction) and synchronization errors thatrepresent an average of the instantaneous (repeatable andnon-repeatable) positional offsets of the wafer and reticle stage.

Because the reticle and wafer move in a coordinated manner as rigidbodies relative to one another, lack of coordination will show up asinstantaneous offset errors, (ΔTx, ΔTy)(x,y,ys). Here (ΔTx, ΔTy)(x,y,ys)is the instantaneous translational offset error of the projected imageat the wafer relative to a perfectly placed wafer is a function not onlyof the intra-field coordinate (x,y) but also of the instantaneousposition, ys, of the wafer relative to the center of the scanning slit.FIG. 1 shows the relation of the full scanner field and field centerrelative to the slot center, this relative position is ys. We areconcerned here only with transverse errors of the stage and reticle andso the instantaneous offset vector (ΔTx, ΔTy)(x,y,ys) will depend onlyon the instantaneous translational offset error (ΔX(ys), ΔY(ys)) and theinstantaneous yaw or rotational error θs(ys) as:(ΔTx,ΔTy)(x,y,ys)(ΔX(ys)+θs(ys)*(y−ys), ΔY(ys)−θs(ys)*x)  Equation 3

Another contributor to the instantaneous offset vector will arise fromthe static distortion contribution of the projection lens. Thus if(ΔXs1, ΔYs1)(x,y) is the static lens distortion then its contribution tothe instantaneous offset vector (ΔTx, ΔTy) will be:(ΔTx,ΔTy)(x,y,ys)=(ΔXs1, ΔYs1)(x,y−ys)  Equation 4

The static lens distortion means the intra-field distortion of thescanner as determined when the wafer and reticle stages are not movedwith respect to one another to produce the scanned image field. Thus,the static lens distortion does not include any contribution fromsynchronization or dynamic yaw errors due to the relative motion of thereticle and wafer stages. Referring to FIG. 1, (ΔXs1,ΔYs1)(x,y) isdefined only over the slot width (SW) and slot height (SH). Therefore x,y vary over the rangesx=(−SW/2:SW/2) y=(−SH/2:SH/2)  Equation 5

There are various techniques for determining (ΔXs1,ΔYs1), a veryaccurate technique is described in “Method And Apparatus ForSelf-Referenced Projection Lens Distortion Mapping” (A. H. Smith, B. B.McArthur, R. O. Hunter, Jr., U.S. patent application Ser. No.09/835,201) but this and other techniques for measuring static lensdistortion are not required for the techniques described below.

Combining Equations 3 and 4 give the total contribution to theinstantaneous offset error as:(ΔTx,ΔTy)(x,y,ys)=(ΔXs1,ΔYs1)(x,y−ys)+(ΔX(ys)+θs(ys)*(y−ys),ΔY(ys)−θs(ys)*x)  Equation 6Here x,y vary over the entire span of intrafield coordinates;x=(−SW/2:SW/2)y=(−L/2:L/2)  Equation 7while ys varies over the range:ys=(y−SH/2:y+SH/2)  Equation 8Since the projected image suffers a shift only when the slot (or moreprecisely any part of the illuminated slot) is over field position(x,y).

The effect of the projected image is then just a weighted average overthe slot of the instantaneous offsets (ΔTx, ΔTy):(ΔXF,AYF)(x,y)=INT{dys*w(y−ys)*(ΔTx,ΔTy)♦(x,y,ys)}INT{dys*w(y−ys)}  Equation9where;

-   x,y intrafield coordinates, x=(−SW/2:SW/2), y=(−L/2:L/2)-   ys=the position of the center of the scanning slit at a given    instant in time referenced from the nominal die center.-   SW=slot width-   L=scanner field length-   dys=differential amount of the scanner field-   INT { }=integral over the scanner field, integration range extends    from ys=(−(L+SH)/2: (L+SH)/2))-   w(y)=weighting function. In 248 nm resists, typically proportional    to the slot intensity profile scanning slit. 0 for points outside    the slit opening.-   (ΔXF,ΔYF)(x,y)=intrafield distortion. Includes effects of scanning    synchronization error and lens aberrations.

The two distinct parts of (ΔTx,ΔTy) (scanner dynamics (Equation 3) andlens distortion (Equation 4)) are additive and therefore the intrafielddistortion, (ΔXF, ΔYF), can also be divided up into similar parts as:(ΔXF,ΔYF)(x,y)=(ΔxL,ΔyL)(x)+(ΔXS(y), ΔYS(y)−x*dΔYS(y)/dx)  Equation 10where the lens aberration contribution, (ΔxL,ΔyL)(x), is given by;(ΔxL,ΔyL)(x)=INT {dys*w(y−ys)*(ΔXs1,ΔYs1)(x,y−ys)}INT{dys*w(y−ys)}  Equation 11and the scanning dynamics contribution, (ΔXS(y),ΔYS(y)−x*dΔYS(y)/dx), isgiven by;(ΔXS(y),ΔYS(y)−x*dΔYS(y)/dx)=INT{dys*w(y−ys)*(ΔX(ys)+θs(ys)*(y−ys),ΔY(ys)−θs(ys)*x)}/INT{dys*w(y−ys)}  Equation 12

Identifying separate components in Equations 11 and 12 gives theindividual expressions for the various components of overlay error. Thusthe dynamic slip in the x and y directions due to synchronization erroris given by;ΔXS(y)=dynamic slip in the xdirection=INT{dys*w(ys)*ΔX(y−ys)}/INT{dys*w(ys)}  Equation 13ΔYS(y)=dynamic slip in the ydirection=INT{dys*w(ys)*ΔY(y−ys)}/INT{dys*w(ys)}  Equation 14the dynamic yaw or rotational error due to synchronization error isgiven by;dΔYS(y)/dx=dynamic yaw ═INT{dys*w(ys)*θs(ys))}/INT{dys*w(ys)}  Equation15

The influence of the dynamic lens distortions on the intra-field error,(ΔxL, ΔyL), is given by;ΔxL(y)=dynamic lens distortion in the xdirection=INT{dys*w(ys)*ΔXs1(y−ys)}/INT{dys*w(ys)}  Equation 16ΔyL(y)=dynamic lens distortion in the y direction=INT{dys*w(ys)*ΔYs1(y−ys)}/INT {dys*w(ys)}  Equation 17

The interpretation of the structure of the intra-field distortion, (ΔXF,ΔYF), is best understood with reference to Equation 10. There, theintra-field distortion is divided into a contribution by the dynamiclens distortion, (ΔxL, ΔyL), that depends only on the cross scancoordinate, x, and is independent of the position along the scanningdirection, y. From Equations 16 and 17, the dynamic lens distortion is aweighted average of the static lens distortion where the weightingfactor, w(y), depends on the intensity distribution in the scandirection, y, possibly the photoresist process, and the scanningdirection. Because the dynamic lens distortion contains none of theeffects of scanning synchronization errors and only effects that arehighly repeatable, the dynamic lens distortion will not vary from scanto scan. Thus, the contribution of dynamic lens distortion to theintrafield distortion can be some arbitrary set of vector displacementsalong a single scan row but will be the same for all rows in the scan,see FIG. 4.

The other contributor to intra-field distortion in Equation 3g) is thedynamic slip and yaw errors, ΔXS(y), ΔYS(y), dΔYS(y)/dx, which depend onthe position along the scanning direction, y, and are independent of thecross scan coordinate, x. From Equations 3j), 3k), 3l) the dynamic slipand yaw are convolutions of the weighting factor w(y) with theinstantaneous translational and yaw offsets. Because dynamic slip andyaw contain nothing but the effects of scanner synchronization error,they will contain both repeatable parts that do not vary from scan toscan and non-repeatable parts that vary from scan to scan. Referring toFIG. 5, each row of the scan will have different translation androtation errors that are generally different and strongly correlatedonly over distances less than about SH, the slot height.

In summary; in the presence of both lens distortion and scannersynchronization error the total overlay distortion error, [δ×(x,y),δY(x,y)] can be expressed in the following form;δX(x,y)=ΔXS(y)+ΔxL(x),  Equation 18δY(x,y)=ΔYS(y)+ΔyL(x)−x*dΔYS(y)/dx  Equation 19

In acid catalyzed photoresists such as those used for KrF or 248 nmlithography, the weighting function will typically be directlyproportional to the intensity of light, I(y), across the slot since thelatent acid image does not saturate until at very high exposure doses.However, in typical I-line photoresists the latent image saturates atnormal exposure doses. This means that at a given location on thephotoresist, the exposing light that first impinges consumes a largerportion of the photoactive material than an equal amount of exposinglight impinging at a later time. Thus the w(y) will not be proportionalto I(y) any longer. Because of this saturation effect, the weightingfunction will depend not only on the photoresist exposure dose used butalso on the scanning direction (positive y or negative y).

First Embodiment

A method for determining the distortion associated with scannersynchronization error (scan error for short) to within a translation,rotation, and skew in the presence of scanner lens distortion isdescribed. The process flow for the first embodiment is diagramed inFIG. 12.

Provide Reticle

Referring to FIG. 6, a reticle, OL, with an (Mx×My) array of overlaygroups, OG, is provided, loaded into a projection lithography tool(machine) being measured, and aligned to reticle alignment mark RM.Reticle OL, shown in cross section in FIG. 11, may be a glass or fusedsilica reticle with a chrome coating that defines the overlay groups,OG; it is a binary mask. FIGS. 7 and 9 show realizations of OG for thefirst embodiment. They both consist of alignment attributes, AA, andcomplementary alignment attributes, AA′, offset from AA a distance M*dp.When overlaid one on top of another, AA and AA′ form completed alignmentattributes, CAA, illustrated in FIGS. 8 and 10. FIG. 8 is the completedalignment attribute, CAA, as viewed on the wafer consisting of theprojection of alignment attribute AA and complementary alignmentattribute AA′ of FIG. 7 on top of one another. The inner square torus ofFIG. 8 represents the projection of AA′ while the outer square torusrepresents the projection of AA onto the wafer. The darkened areasrepresent exposed photoresist or other recording media.

FIG. 7 is a realization of overlay group OG for a dark field mask. Thedarkened areas represent chrome removed from the reticle and typicaldimensions in microns are shown. These dimensions are appropriate whenoverlay reticle OL is used in a 4:1 (M=4 in FIG. 6) or 5:1 (M=5 in FIG.6) reduction imaging tool. When used in a 1:1 imaging tool (nomagnification or demagnification of the image size) the dimensions shownin FIG. 7 would be reduced by approximately 4-5 times so that thecompleted alignment attributes (CAA of FIG. 8) would be within therecommended size range for bar in bar structures suitable for an overlaymetrology tool, typically about 15-30 um. See Overlay Target Design,KLA-Tencor, KLA-Tencor, 1:4, 1996. M*dp of FIG. 6 is the distancebetween alignment attributes AA and their complements AA′ and for theexample of FIG. 7 is equal to 500 microns.

FIG. 9 is another realization of overlay group OG, this time for abright field mask. The darkened areas represent chrome remaining on thereticle and typical dimensions in microns are shown. These dimensionsare appropriate when overlay reticle OL is used in a 4:1 (M=4 in FIG. 6)or 5:1 (M=5 in FIG. 6) reduction imaging tool. The same comments aboveapply to the design basis for this size and adaptation to imaging toolswith other magnifications, M. M*dp of FIG. 6 is the distance betweenalignment attributes AA and their complements AA′ and for the example ofFIG. 9 is equal to 500 microns. FIG. 10 is the completed alignmentattribute, CAA, as viewed on the wafer consisting of the projection ofalignment attribute AA and complementary alignment attribute AA′ of FIG.9 on top of one another. The inner square box of FIG. 8 represents theprojection of AA′ while the outer square box represents the projectionof AA onto the wafer. The darkened areas represent resist remaining onthe wafer, in the case of a positive tone resist.

Referring to FIG. 6, overlay groups OG are separated a distance M*p″where p″ is typically in the range of 0.5 mm to 10 mm when used onsemiconductor wafers. M is the reduction magnification ratio of theprojection imaging tool used. For semiconductor manufacturing this istypically M=1, 4 or 5, most commonly 4 or 5. Thus an exemplary dimensionfor M*p″ for an M=4 or M=5 system is 4 mm leading to a pitch, p″, of theprojected pattern on the wafer of p″=1 mm (M=4) or p″=0.8 mm (M=5).Typical values for p″ are in the range of 0.5 mm to 10 mm while typicalvalues for dp are 0.02 mm to 1 mm. The significant constraint on p″ isthat it be small enough to provide detailed enough coverage of the scandistortion pattern. Stated differently, we need to sample the scandistortion at a fine enough interval such that the distortions at theunmeasured locations in between the overlay groups are reasonablyapproximated (error less than 30% maximum distortion) by interpolatingthe values of scan distortion measured on pitch p″. The significantconstraint on offset dp is that it lie within an area where the scandistortion is not varying significantly. Stated differently, the overlaygroup of FIG. 6 should lie within an isoplanatic distortion patch of thescan field, herein defined as being a region over which the scannerdistortion varies by less than about 5% of the maximum value of the scandistortion.

Also disposed on overlay reticle OL will be reticle alignment marks, RM,that allow the reticle to be precisely aligned with respect to theprojection imaging tool it is used on.

The number of overlay groups OG on reticle OL is determined by themaximum projected field size of the machine or set of machines we willbe measuring. In cases where the extent of the overlay groups on thereticle exceeds the size of the maximum field, the entire Mx×My array isnot required, a smaller section that fits within the maximum field orother user designated field will work with the method of this invention.

Load/Align Reticle

Next, overlay reticle OL is loaded into the projection lithography tool(machine) and aligned. The reticle alignment is typically carried outusing reticle alignment marks, RM. On lower accuracy machines, largeralignment attributes AA and their complements, AA′, when combined withmechanical banking or placement of the reticle may suffice for reticlealignment. In these circumstances, no reticle alignment marks would berequired.

Provide/Load/Align Wafer

Next, a photoresist coated wafer is provided. Referring to FIG. 16, thiswafer may have already disposed on it global wafer alignment marks GM0and GM90. GM0 is the wafer alignment mark suitable for the wafer when itis loaded with the notch in the default or 0 degree orientation. Twomarks, shown in FIG. 16, and possibly more, are typically required forwafer alignment. The required alignment accuracy for semiconductorwafers and standard box in box or bar in bar completed alignmentattributes will typically be less than about 2 um. This is so theoverlay tool metrology used for measuring the completed alignmentattributes is operating in the regime where it is most accurate andrepeatable. See KLA 5105 Overlay Brochure, KLA-Tencor. GM90 is thealignment mark suitable for the wafer when loaded with the notch in therotated 90 degrees from the default or 0 degree orientation. Two marksare shown in FIG. 16. In cases where the wafer prealignment system canmeet the required tolerances by aligning off of the wafer edge andnotch, an unpatterned wafer can be used. Once provided, the wafer isthen loaded and aligned on the projection lithography tool we aremeasuring.

Expose Reticle

Next, referring to FIG. 17, overlay reticle OL is exposed projecting anNx×Ny array of overlay groups, OG, from reticle OL onto wafer Wresulting in an Nx×Ny array of projected overlay groups, POG, on waferW. The entire projected array comprises a field F over which we will bemeasuring the machine dynamic scan distortion; the present inventionwill determine the synchronization or dynamic distortion present in thissingle realization of scanning distortion as present in the field F.

Rotate/Align Wafer

Following the first exposure the wafer is rotated by 90 degrees andrealigned using global wafer alignment marks GM90. For the rotationstep, the wafer may have to pass out through the track, skipping theresist development cycle and be passed back through track, skipping theresist coating cycle, and reinserted onto the wafer chuck. In somecases, the wafer may need to be rotated by hand approximately 90 degreesbefore the machine prealignment system can accommodate it. In any event,once the wafer has been rotated, it is then aligned as discussed aboveonly the GM90 marks are utilized. In this case the global waferalignment marks GM0 remain individually identical in appearance oncethey have been rotated by 90 degrees, then in their new position theycan serve the same function as marks GM90. For the purposes of thisinvention the wafer can be rotated either clockwise or counterclockwiseby 90 degrees. The description of the preferred embodiment assumes thewafer is rotated clockwise by 90 degrees as indicated by FIG. 27.

Expose OL Reticle To Create Completed Alignment Attributes

Next the wafer is exposed with the overlay reticle OL one or more timesresulting in an Nx×Ny array of projected overlapped overlay groupsconsisting of one or more of the following types, OLAP1, OLAP2 or OLAP3,(See FIGS. 18 and 34). Referring to FIG. 15, field F is shown as adashed rectangle longer than it is wide and with the scanning directionindicated by an arrow. This is typical of the dimensions of a scannedfield since the purpose of the scanning mechanism is to enlarge theprojected imaging field by utilizing the mechanical synchronization ofthe wafer and reticle stage and thereby minimize the area projected byimaging objective. See Optical Lithography—Thirty Years and Three Ordersof Magnitude, J. Bruning, SPIE Vol. 3051, 14:27, 1997. Typical maximumscanned field dimensions for semiconductor wafer scanners are 22×32.5,25×33, 26×33, and 26×34 is (SW×L in mm per FIG. 1). Thus forsemiconductor wafer scanners, to create completed alignment attributesat all Nx×Ny projected overlay groups two separate scans (with fields R1and R2 in FIG. 15) are required. While the fields R1 and R2 could bedone without any overlay region, OL, the resulting measurement set ofcompleted alignment attributes could only partially determine thedynamic scan error over the entire field. While this can be useful inthe case where only a small portion of the entire scanned field is to beanalyzed or the projected field of interest is small enough that only asingle field, R1, will overlay the field of interest, F, the overlapping2-field case represents the preferred embodiment. Cases where fewer ormore fields are required to overlap F are easily adapted from thisembodiment. FIG. 20 explicitly shows which overlay groups in FIG. 18result from which exposure first, R1, R2).

When viewed with the notch at nominal or 0 degree orientation, (See FIG.18), exposure R1 of reticle OL of FIG. 6 consists of an Nx×Ny′ array ofoverlay groups (dashed lines of FIG. 18) placed to form completedalignment attributes, CAAL, when combined with the overlay groupsdefined by the field F exposure (solid lines of FIG. 18). Ny′ is lessthan Ny allowing R1 to be placed so. If the field F has been exposedwith center located at wafer coordinates (xc,yc) then for the reticlelayout of FIG. 6, then the center of exposure R1 will be made atexposure coordinates (FIG. 27) (xe,ye)=(yc−p″*(Ny−Ny′)/2−dp, −xc).Exposure coordinates (xe,ye) do not rotate with the wafer but coincidewith the wafer coordinates when the wafer has its notch at the 0 degreeor nominal orientation. Both wafer and exposure coordinates have thewafer center, WC of FIG. 27, as their origin. So, having completed theR1 exposure, there results an Nx× Ny′ array of completed alignmentattributes for the lower portion of the field F (CAAL of FIG. 18).

Next, exposure R2 is made covering the upper portion of field F andconsisting of an Nx×Ny″ array of overlay groups (dash dot lines of FIG.18) that are placed to form an Nx×Ny″ array of completed alignmentattributes, CAAU, for the upper portion of field F. Ny″ is less than Nyso the CAAU array extends from row b=Ny−Ny″+1 to b=Ny. So that we candiagnose the scan distortion over the entire field F, the lower andupper exposures, R1 and R2, need to overlap at least two overlay groups.Referring to FIG. 18, rows b=Ny−Ny″+1 through b=Ny′ will consist ofprojected overlapped overlay groups OLAP2 each of which consists ofcompleted alignment attributes CAAL and CAAU. In terms of Ny′ and Ny″this means Ny′+Ny″>=Ny+2. With the field F placed at (xc,yc), exposureR2 will be placed at exposure coordinate (xe,ye) (yc+p″*(Ny−Ny″)/2+dp,−xc) resulting in the dash dot overlay groups of FIG. 18.

The net result of exposures F, R1 and R2 is to create an Nx×Ny−Ny″ arrayof projected overlapped overlay groups, OLAP1, each containing at leastone completed alignment attribute, CAAL, of fields F and R1. Further, anNx×Ny′−Ny+Ny″ array of projected overlapped overlay groups, OLAP2, eachcontaining at least one completed alignment attribute, CAAL, of fields Fand R1 and at least one completed alignment attribute, CAAU, of fields Fand R2. Further, an Nx×Ny−Ny′+1 array of projected overlapped overlaygroups, OLAP3, each containing at least one completed alignmentattribute, CAAU, of fields F and R2.

Develop Wafer

The wafer is then developed.

Measure Overlay Targets

Next, an overlay metrology tool is used to determine the positionaloffset error of at least two columns of completed alignment attributes.Thus, in the first embodiment, the two outer columns, a=1 and a=Nx ofFIG. 18 would be measured. Within each measured column, all completedalignment attributes, Ny′CAAL and Ny″ CAAU, for a total of Ny′+Ny″ wouldbe measured. The effect of not measuring an alignment attribute CAAL orCAAU is that we lose information concerning scanner distortion for thatparticular row, however we need to measure at least two rows where thealignment attributes lie within OLAP2 groups.

Provide Lens Distortion Map

Next, a map of the dynamic lens distortion for the machine beingmeasured is provided. The dynamic lens distortion (Equation 4)represents the effect of lens aberrations on intrafield distortion. Lensdistortion is constant over short time periods (less than about one day)and therefore its contribution can be determined in advance and used forcorrections and improvements in accuracy for the present determinationof scanning distortion.

There are numerous methods for determining dynamic lens distortion themost accurate of which is the method of Smith, (“Method and ApparatusFor Self-Referenced Dynamic Step And Scan Intra-Field Lens Distortion”,U.S. Pat. No. 6,906,780). Another technique for the determination oflens distortion is the method of Smith, McArthur, and Hunter (“MethodAnd Apparatus For Self-Referenced Projection Lens Distortion Mapping”,U.S. patent application Ser. No. 09/835,201, now-U.S. Pat. No.6,573,986). This technique can be applied to measure the repeatable partof the scanner distortion along with the lens distortion, the resulting2-dimensional field fit to the functional form for scanner intra-fielddistortion (Equation 10) and the dynamic lens distortion extracted. Yetanother technique involves exposing a dynamic field a single time andmeasuring the absolute positions of the printed features using anabsolute position metrology tool such as the LMS IPRO. See Leica LMSIPRO Brochure, supra. Again, the resulting 2-dimensional field fit tothe functional form for scanner intra-field distortion (Equation 10) andthe dynamic lens distortion extracted.

In cases where the scanning distortion is large compared to the lensdistortion, the contribution from lens distortion can be neglected.

Reconstruct Scanner Distortion Map

At this point, a software algorithm is used to calculate the scannerdistortion the result being a table, as shown in FIG. 14, consisting ofthe scanning distortion as a function of the scan (y) position. Whatfollows are details of the software algorithm.

As noted above, and repeated here, Equations 18 and 19 show that theintrafield distortion error in the presence of scanner synchronizationerror and lens distortion is the sum of two vector parts;δX(x,y)=ΔXS(y)+ΔxL(x),  Equation 18δY(x,y)=ΔYS(y)+ΔyL(x)−ΔYR(x,y)  Equation 19

Where (x, y) are the intrafield coordinates. They are centered on fieldF and shown in FIG. 19. Also, ΔXS(y), ΔYS(y), represent the integratedaverage translational error associated with the scanning dynamics,ΔxL(x), ΔyL(x), represent the translational error associated with lensdistortion and ΔYR(x,y) represents the integrated scanning average Yawerror (ΔYR(x,y)=x*[dΔYS(y)/dx]=x*[θavg(y)]).

The deviation of the overlay groups in field F from their idealpositions (dxF,dyF)(x,y) is given by:dxF(x,y)=Tx−q*y+ΔxL(x)+ΔXS(y)  Equation 20dyF(x,y)=Ty+q*x+ΔyL(x)+ΔYS(y)+x*θavg(y)  Equation 21where Tx, Ty, q represent a gross intrafield translation and rotationdue to reticle and stage mispositioning.

The deviation of the overlay groups in field R1 from their idealpositions (dxR1,dyR1)(x,y) is given by:dxR 1(x,y)=Tx′−q′*y−ΔyL(y+n1*p″)+ΔYS′(x)+y*θ′avg(x)  Equation 22dyR 1(x,y)=Ty′+q′*x+ΔxL(y+n1*p″)+ΔXS′(x)  Equation 23where n1=when field R1 is centered within the maximum allowed exposurefield and T{dot over (x)}′, Ty′, q′ are another set of translations androtation.

The deviation of the overlay groups in field R2 from their idealpositions (dxR2,dyR2)(x,y) is given by:dxR 2(x,y)=Tx″−q″*y−ΔyL(y−n2*p″)+ΔYS′(x)+y*θ″avg(x)  Equation 24dyR2(x,y)=Ty″+q″*x+ΔxL(y−n2*p″)+ΔXS″(x)  Equation 25where n2=when field R2 is centered within the maximum allowed exposurefield and Tx″, Ty″, q″ are yet another set of translations and rotation.

Denoting now the sign of the displacement for the outer box by + and thesign of the inner box by −, the lower completed alignment attributes,CAAL, produce overlay measurements:BBx(x,y;L)=Tx−Tx′+ΔxL(x)−ΔYS′(x)+(−q+q′−θ′avg(x))*y+ΔyL(y+n1*p″)+ΔXS(y)  Equation 26BBy(x,y;L)=Ty−Ty′+ΔyL(x)−ΔXS′(x)+(q−q′+θavg(y))*x−ΔxL(y+n1*p″)+ΔYS(y)  Equation 27while the upper completed alignment attributes, CAAU, produce overlaymeasurements:BBx(x,y;U)=Tx−Tx″+ΔxL(x)−ΔYS″(x)+(−q+q″−θ″avg(x))*y+ΔyL(y−n2*p″)+ΔXS(y)  Equation 28BBy(x,y;U)=Ty−Ty″+ΔyL(x)−ΔXS″(x)+(q−q″+θavg(y))*x−ΔxL(y−n2*p″)+ΔYS(y)  Equation 29

In the region where R1 and R2 overlap the projected overlay groups,OLAP2, contain both an upper, CAAU, and lower, CAAL, completed alignmentattribute. The difference between the upper and lower overlaymeasurements at the same position and putting the known lens distortionson the left hand side gives:BBx(x,y;U)−BBx(x,y;L)−ΔyL(y−n2*p″)−ΔyL(y+n1*p″)=Tx″+Tx′−ΔYS″(x)+ΔYS′(x)+(q″−q′−θ″avg(x)+θavg(x))*y  Equation30BBy(x,y;U)−BBy(x,y;L)−ΔyL(y−n2*p″)−ΔyL(y+n1*p″)=−Ty″+Tx′−ΔXS″(x)+ΔXS′(x)+(−q″+q′)*y  Equation31The interpretation of Equations 30 and 31 is that we know thetranslation and rotation of each column in the upper section relative tothe lower section and that therefore, by applying Equations 30 and 31 attwo or more points in y along each column, we can fix the location ofthe lower set of completed alignment attributes, CAAL, to the uppersection of completed alignment attributes, CAAU.

Further interpreting Equations 26-29, considering a specific column orfixed x value, since the uncertainty or unknown part of the lensdistortion will typically consist of a translation, rotation andx-scale. Based on these unknown quantities, and utilizing data from twodistinct columns (y values) of field F, we will be able to determineΔXS(y) to within an expression of the form a+b*y, θavg(y) to within aconstant d, and ΔYS(y) to within a constant c. Taken altogether, we willbe able to determine the scanner distortion (ΔXS(y), ΔYS(y)+θavg(y)*x)to within an expression of the form (a+b*y,c+d*x) where a,b,c,d areunknown constants. In other words, we will know the scanning distortionto within a translation, rotation and skew (b term).

Equations 26-29 are typically solved using the singular valuedecomposition to produce the minimum length solution. See NumericalRecipes, The Art of Scientific Computing, W. Press et al., CambridgeUniversity Press, 52:64, 1900. They are typically over-determined in thesense of equation counting (there are more equations than unknowns) butare still singular in the mathematical sense; there is an ambiguity inthe solution of these equations. This ambiguity in the four parameterset discussed above for the wafer stage can also induce intrafieldrotation errors.

At this point we have accomplished the last step in the process of thisinvention and we can record the final results of the scanning distortionin tabular form (FIG. 14).

Second Embodiment

Instead of the reticle of FIG. 6, this invention could be carried outwith the reticle layout of FIG. 13. It too consists of an Mx×My array ofoverlay groups OG on regular pitch M*p″ the only difference being in thedetails of the overlay group. Now overlay group OG consists of alignmentattribute AA and only a single complementary alignment attribute, AA′,offset from it in a single direction. An example of an overlay groupwith this structure is shown in FIG. 21. There a dark field reticledesign consists of outer bar alignment attribute AA and thecomplementary alignment attribute consists of an inner bar alignmentattribute AA′. Reticle dimensions suitable for an M=4 or 5 reductionimaging lithography tool are shown. FIG. 22 shows how projectedoverlapped overlay groups OLAP1, OLAP2 and OLAP3 of FIG. 18 would appearwhen the overlay group of FIG. 21 is utilized. Lower, CAAL, and upper,CAAU, completed alignment attributes are also indicated. The dark areascorrespond to exposed resist. Other than the appearance of the overlaygroups, this reticle would be used in the same way as the reticlementioned in the preferred embodiment.

Third Embodiment

In this case, the overlay groups OG of reticle OL (FIG. 6) consist of apair of wafer alignment marks. Referring to FIG. 23, overlay group OGconsists of alignment attribute AA and offset from it is complementaryalignment attribute AA′. AA is a wafer alignment mark, WAM0, suitablefor use by a lithography tool wafer alignment system and stage when thewafer is in the nominal or 0 degree position. AA′ is a wafer alignmentmark, WAM90, which is wafer alignment mark WAM0 rotated by 90 degrees ina clockwise direction. FIG. 24 shows how projected overlapped overlaygroups OLAP1, OLAP2 and OLAP3 of FIG. 18 would appear when the overlaygroup of FIG. 23 is utilized. Lower, CAAL, and upper, CAAU, completedalignment attributes are also indicated. The exposure steps of thepreferred embodiment must be altered is an obvious way so the waferpattern results in the projected overlapped overlay groups OLAP1, OLAP2and OLAP3 of FIG. 24. The other step that differs in detail is that ofmeasuring the overlay targets. In this instance, instead of using anoptical overlay metrology tool, the lithography tool wafer stage andalignment system is used. The completed alignment attribute is a pair ofwafer alignment marks (FIG. 3 and CAAL, CAAU of FIG. 24) and thelithography system measures the offset of the two alignment marks AA′and AA and the nominal offset, (D,0), is subtracted from this resultingin the required overlay measurement. The nominal offset, (D,0), isdetermined by the details of the exposure plan and the minimumseparation requirements of the wafer alignment system. Typically, D isless than about 0.5-1 mm so that the wafer stage is utilized overextremely small distances where it's accuracy will be greatest. So, whenreferring to overlay metrology tools, we also encompass absolutepositioning metrology tools used over small (<4 mm) distances. Waferalignment mark WAM need not be the same wafer alignment mark as themachine we are measuring, it could be another absolute positioningmetrology tool. This embodiment is useful for embedding the entireprocedure and technique of this invention into a lithography tool forself-analysis.

Fourth Embodiment

In this case, the overlay groups OG of reticle OL (FIG. 6) consists of asingle wafer alignment mark. Referring to FIG. 25, overlay group OGconsists of alignment attribute AA which is complementary to itself whenrotated by 90 degrees. WAM is a wafer alignment mark suitable for use bya lithography tool wafer alignment system. FIG. 26 shows how projectedoverlapped overlay groups OLAP1, OLAP2 and OLAP3 of FIG. 18 would appearwhen the overlay group of FIG. 25 is utilized. Lower, CAAL, and upper,CAAU, completed alignment attributes are also indicated. The exposuresteps of the preferred embodiment must be altered is an obvious way sothe wafer pattern results in the projected overlapped overlay groupsOLAP1, OLAP2 and OLAP3 of FIG. 26. The detailed method and descriptionof measuring the completed alignment attributes is as described in thethird embodiment. This embodiment is extremely useful when the procedureand technique is embedded into the projection imaging tool for use inself-analysis.

Fifth Embodiment

FIG. 28 shows a fifth embodiment constructed in accordance with thisinvention. When it is desired to measure the repeatable part of thedynamic scan distortion with a minimum number of overlay measurements,the two reticles are used. The first reticle, OL, is the one alreadydescribed above. The second reticle, OL′, is the reticle of FIG. 6 asmodified with the addition of a partially reflecting coating, PR, to thesurface opposite the patterned chrome surface (FIG. 28). There,partially reflecting coating PR will typically reflect 50% to 99% of theincident light used for resist exposure while patterned chrome surface,PS, contains overlay groups OG. Thus, overlay reticle OL′ is a reducedtransmission reticle, meaning it's transmission is less than that of anormal reticle. In operation, the step of “Expose Reticle” whichproduces field F of FIG. 17 is carried out with reticle OL′. Now insteadof a single exposure, because of the reduced net reticle transmission(as produced by partially reflecting coating PR), multiple exposures aremade so the resist receives the correct clearing dose. The effect ofdoing N exposures to make field F is that the non-repeatable part of thedynamic scan distortion is averaged over a number of exposuresproportional to N thereby reducing its contribution to the net dynamicscan distortion. After the “Expose Reticle” step has been carried out,the remaining steps, as previously described, are carried out. Inparticular, the step of “Expose OL Reticle to Create Completed AlignmentAttributes” is carried out using ordinary reticle OL.

Sixth Embodiment

FIG. 29 shows a sixth embodiment constructed in accordance with thisinvention. This is another specific variation of the reducedtransmission reticle, OL′, of the fifth embodiment only now instead ofhaving a partially reflecting coating on the back side, the patternedface that contains the overlay groups, OG, is patterned as an attenuatedphase shift mask. See The Attenuated Phase Shift Mask, B. Lin, SolidState Technology, Special Series/Advanced Lithography, 35(1):43-47,(January, 1992). The overlay groups are patterned using only theattenuated phase shifting material. It is not the phase shiftingproperty of this layer that is significant only its transmissioncharacteristics which are typically less than about 10%. In all otherrespects, this embodiment is identical to the fifth embodiment.

Seventh Embodiment

FIG. 30 shows a seventh embodiment constructed in accordance with thisinvention. Here instead of reticle OL of FIG. 6 being a transmissivereticle it is a reflective reticle. In a dark field version of this(FIG. 30) the overlay groups are defined by the presence of a reflectivelayer on the mask.

Embodiments for Determining Wafer Stage Grid and Yaw for IndividualScans

Wafer stage grid and yaw is an important source of overlay error (see A.Smith et al., “Method and Apparatus for Self-Referenced Wafer StagePositional Error Mapping”, U.S. Pat. No. 6,734,971, May 11, 2004). Waferstage grid and yaw refer to the overlay error contributed by the waferstage in translation (tx,ty) and rotation (q) in moving from oneprojection field to another; and is commonly referred to referred to aswafer stage error. Self-referenced techniques for measuring therepeatable part of it on scanners are described in “Method and Apparatusfor Self-Referenced Wafer Stage Positional Error Mapping”, supra. Thesetechniques can be used to determine the average or repeatable behaviorof stage grid and yaw which is an important component of the errorbecause it can be corrected for either internally within the scanner orusing production job decks that are customized to particular machines byincorporating known wafer stage errors.

Statistical analysis and correlations of wafer stage grid and yaw arevaluable, for example, for machine trouble shooting, machineclassification and machine emulation (see A. Smith et al., “Method ofEmulation of Lithographic Projection Tools”, U.S. application Ser. No.11/111,302, Apr. 20, 2005 claiming priority to U.S. Provisional PatentApplication No. 60/564,094, Apr. 20, 2004). The ability to measure thewafer stage error for individual scans improves the gathering andcompiling of meaningful statistics. Thus, it would be desirable to havea self-referenced technique that can determine the wafer stage grid andyaw for individual scans on a step and scan projection lithography tool.

FIG. 35 is a flow chart illustrating a technique for measurement ofwafer stage grid and yaw errors. Flow begins in Block 3502 where a waferis provided. The wafer includes two sets of alignment marks, one set forproduction notch angle, and another set for use at 90 degrees from theproduction angle. Flow continues to Block 3504 where an overlay reticleis provided. Flow continues to Block 3506.

In Block 3506 the reticle is exposed onto the wafer in accordance with amodified production layout scheme. Flow continues to Block 3508 wherethe reticle is exposed to create horizontal cross ties. Flow continuesto Block 3510. In Block 3510 the wafer is rotated 90°. The reticle isexposed to create vertical cross ties. Flow continues to Block 3512.

In Block 3512 the exposed overlay targets are measured for location.Flow continues to Block 3514 where dynamic intra-field lens distortionis provided using the overlay target measurements. Flow continues toBlock 3516 where a wafer stage grid and yaw error are reconstructed.

FIG. 36 is a schematic illustrating a wafer with wafer alignment markssuitable for alignment at two notch angles offset by 90 degrees fromeach other as described in Block 3502 of FIG. 35. As shown in FIG. 35,one set of wafer alignment marks (WAMs) is used for wafer alignment withthe wafer in notch down (Qnotch 270°) position. The other set of WAMs isused when the wafer is rotated by 90 degrees (Qnotch=0°). The WAMs aretypically etched into the wafer W.

FIG. 37 is a plan view of a portion of a reticle, as could be used inBlock 3504 of FIG. 35, illustrating sets of overlay groups (OLG). Asshown in FIG. 37, a portion of the reticle R includes an NRX×NRY set ofoverlay groups, OLG, on a pitch P′. The reticle illustrated in FIG. 37is similar to that described in A. Smith et al., “Method and Apparatusfor Self-Referenced Projection Lens Distortion Mapping”, U.S. Pat. No.6,573,986, Jun. 2, 2003.

FIG. 38 is a schematic illustrating further details of an exemplaryoverlay alignment group. In the exemplary OLG shown in FIG. 38, theoverlay group OLG is written on a dark field mask where an alignmentattribute (AA) is an outer bar pattern and complimentary alignmentattributes (AA′) are an inner bar pattern. When the AA is printed on thewafer W the resulting structure is referred to as a printed alignmentattribute (PAA). Likewise, when the AA′ is printed it is referred to asa printed complimentary alignment attribute (PAA′). The result ofoverlaying an AA and a AA′ results in a completed alignment attribute(CAA) as discussed further in FIG. 39. The CAA is a structure that canbe read by an overlay metrology tool.

FIG. 39 is a plan view of an exemplary completed alignment attributeprinted at M=4 reduction. As shown in the example of FIG. 39 the CAA ismade up of an AA that is an outer bar, or box, with an AA′ that is aninner bar, or box, located inside the AA outer bar. The resultingstructure illustrated in FIG. 39 is referred to as a bar-in-bar patternand the relative positions of the AA and AA′ can be read by an overlaymetrology tool, such as, a KLA 5200 or other commercial tool. FIG. 39illustrates an example of why features AA and AA′ on a reticle arereferred to as being complementary to one another because the CAA can beread by an overlay tool.

Returning to FIG. 36, the wafer W may be coated with photoresist andloaded onto a scanner projection imaging tool (PIT) described in FIG. 47below. The overlay reticle R is exposed with a field size, dose, andfield layout that mimics the product layout, as described in Block 3506in FIG. 35, above. An advantage for duplicating production runs in asmany aspects as possible is that it replicates stage exposure dynamicsas product wafers experience it. A production field pattern is generallya rectangular grid of field centers (most common) or the fields areshifted from row to row (or possibly from column to column) by somemultiple of the die pitch. This shifting is typically done to try tomaximize the number of good die. The location of the center of theproduction fields on the wafer (wafer center=0,0) is (XCP, YCP)(IP=1:NF) and the projected field widths are (XWP, YWP). A modificationmade for the overlay reticle R exposure sequence is to snap its exposurecenters to a grid with the same pitch as the projected overlay grouppitch P=P′/M. Thus, the locations of the field centers on the wafer willbe: $\begin{matrix}{{\left( {{XC},{YC}} \right)({IP})} = {P*\left( {{{NINT}\left( \frac{{XWP}({IP})}{P} \right)},{{NINT}\left( \frac{{XWP}({IP})}{P} \right)}} \right)}} & {{Equation}\quad 32}\end{matrix}$NINT=nearest integer function and the exposure width will be reducedslightly so that no partial overlay groups are exposed: $\begin{matrix}{{\left( {{XW},{YW}} \right) = {2*P*\left( {{INT}\left( {\frac{XWP}{2}*P} \right)} \right)}},{{{INT}\left( {\frac{XWP}{2}*P} \right)} + {4*G}}} & {{Equation}\quad 33} \\{\quad{{{where}\text{:}\quad G} = \frac{G^{\prime}}{M}}} & {{Equation}\quad 34}\end{matrix}$

This technique results in putting down a regular grid (possibly withmissing rows and columns) of printed overlay groups with a pitch=P.

FIG. 40 is a schematic illustrating a wafer after exposure of an overlayreticle according to a modified production plan layout. FIG. 40 showswafer W after printing overlay reticle R four times resulting in printedfields PF1:PF4. The resulting printed overlay groups, POLG, are locatedon a two-dimensional grid of pitch P with a missing column at XW=0 and amissing row at YW=0. Wafer alignment marks WAM were used to print thiswafer in the notch down (Qnotch=0°) orientation. The wafer stagetranslation and rotation present in the fields printed in this exposurestep (PF1:PF4 in FIG. 40) will be determined.

The overlay reticle R is now exposed to create so-called horizontalcross ties or HCT, as described in Block 3508 in FIG. 35, above. Becausethe overlay reticle R was printed so that overlay groups OLG are onregular pitch P, additional exposures can be performed such that eachrow of the printed overlay groups from the modified production exposure,described above, has adjacent printed fields, PF, tied together at aminimum of two sites in each printed field per adjacent printed field.For example, in FIG. 40, row RW located at YW=−P contains POLG fromprinted fields PF1 and PF2.

FIG. 41 shows the first horizontal cross tie exposure (HCTE1) whichplaces the field center of a 5×5 central section of overlay reticle R atwafer coordinates (XW,YW) (G, −3P) and creates horizontal cross ties forrows 1:5 (i.e., rows with YW=−5P, −4P, −3P, −2P, −P). The next HCTexposure, HCTE2, creates the horizontal cross ties for rows at YW=P:5P.This would complete the HCT exposures for the wafer of FIG. 41. Thereare a total of ten HCT in FIG. 41 of which one, HCT 1/10, is explicitlycalled out. It overlaps two POLG in PF1 (POLG located at XW=−2P, −P) andtwo POLG in PF2 (POLG located at XW=P, 2P). In general, each HCTexposure will overlap two adjacent printed fields and within eachadjacent field it will need to overlap a minimum of two POLG (more arebetter, vide infra).

After exposing the HCT, each row of printed fields form a horizontalcross row, HCR, of which one (HCR 1/10) is shown in FIG. 41 surroundedby a dashed line. Another example is shown in FIG. 42 where portions ofthree printed fields, PF8, PF9, PF10, are tied together by two HCTexposures (HCT15, HCT16) to form horizontal cross row HCR.

Two exposures were made to create the HCT in FIG. 41; this was foreconomy in stepper setup. Likewise, ten separate exposures could havebeen performed, one for each HCT in FIG. 41.

Rotate Wafer 90°. Expose Vertical Cross Ties

As described in Block 3510 in FIG. 35, after the horizontal cross tieshave been created, the wafer W may be rotated 90 degrees and aligned towafer alignment marks WAM90 (see FIG. 43). After alignment, verticalcross ties, VCT, are exposed to create two or more vertical crosscolumns (VCC1 & VCC2). FIG. 43 is a schematic illustrating a wafer afterexposure of vertical cross ties. In FIG. 43, the VCT exposures areindicated by dashed and bold gray overlay groups and by themselves (thatis without considering the POLG created in Block 3506 in FIG. 35) formstructures that are analogous to the HCR of FIG. 41, but rotated by 90°.In illustration, rotating FIG. 43 by 90 degrees counter clockwise andlooking only at the dashed and bold gray POLGs, there is a structuresimilar to HCR1/10 of FIG. 41. Thus, each VCC forms an interlocked linewith an overlap of at least two POLG per scan row exposure. For theexample shown in FIG. 43, VCC1 is made by three separate VCT exposures,where one of the exposures (shown in bold gray) forms interlocking POLGs(IPOLGs) joining PF1 with PF3.

As shown in FIG. 43, each VCC also overlaps every POLG printed duringthe modified production plan layout (see Block 3506 of FIG. 35) withinthe VCC's column. Referring again to FIG. 43, printed complimentaryalignment attributes, PCAA, in VCC2 overlap all of the printed alignmentattributes (PAA) that are offset from the PCAA in the XW=5P column laiddown in Block 3506 in FIG. 35. Observe the same arrangement in VCC1 ofFIG. 43.

Generally, two VCCs will be adequate in determining wafer stage grid andyaw, however a greater number may lead to better results by providingredundancy that will increase the accuracy of the described techniques.

FIG. 44 is a schematic illustrating a layout of horizontal cross rows(HCR) and vertical cross columns (VCC) on a wafer. As illustrated inFIG. 44, if there are horizontal cross rows, for example, HCR1:HCR14,then only two vertical cross columns VCC2 and VCC3, would be needed toobtain adequate results. However, including additional vertical crosscolumns VCC1 and VCC4 increases the accuracy of the resultingreconstruction.

After exposure of horizontal and vertical cross ties, overlaymeasurements are taken using an overlay metrology tool, such as anAccent Q300 or KLA 5200. The measurements may be conveniently firstdivided up into HCR and VCC sets.

The HCR sets may be indexed by the row number (irow in FIG. 43), crossscan row index (i and i′in FIG. 42) and transverse overlay group indexwithin the scan row (j and j′ in FIG. 42). This organization is based onthe observation that while the reticle and intra-field lens distortionerrors (vide infra) are known, the remaining unknowns are the scansynchronization error combined with the wafer stage grid and yaw and,therefore, each individual scan row (ISR) has a known position to withina translation and rotation. The HCR overlay may be taken and presentedas a five fold indexed array (BBXH,BBYH)(irow;i,j;i′,j′) where:

-   -   irow=cross wafer printed field (Block 3506 in FIG. 35) scan row        number    -   i=independent scan row (ISR) number within irow of printed field        (Block 3506 exposure sequence)    -   j=overlay group column number within ISR I    -   i′=independent scan row (ISR) number within irow of horizontal        cross tie (HCT)    -   j′=overlay group column number within ISR i′.

An example of measurement at a particular site is illustrated in FIG.42, where the irow index has been dropped. In FIG. 42, there are a totalof eight overlay measurements characterized by constant valued indexirow and indices:

-   (i,j;i′,j′)=(1,1;2,−2), (1,2;2,−1), (3,−2;2,1), (3,−1;2,2), (3,    1;4,−2), (3,2;4,−1), (5,−2;4,1), (5,−1;4, 2).

Measurements of VCC may fall into two categories, those used for intraVCC adjustment and inter HCR/VCC adjustment. Intra VCC adjustment issimilar to intra HCR adjustment in that the overlay measurements arebeing used to solve for the individual scan rows (ISR) translation androtation. Intra VCC measurements are denoted(BBXV,BBYV)(ico1;i″,j″;i′″,j′″) where the intra VCC indices(ico1;i″j″;i′″, j′″) mean:

-   -   ico1=VCC column number    -   i″=independent scan row (ISR) number within VCC exposure that        overlays printed field (see Block 3506 in FIG. 35) exposures    -   j″=overlay group column number within ISR i″    -   i′″=independent scan row (ISR) number within VCC exposure that        only overlays other VCC exposures    -   j′″=overlay group column number within ISR i′″.

An example for VCC2 of FIG. 43 is shown in FIG. 45. FIG. 45 is aschematic illustrating indices for a vertical cross column used todescribe an exemplary technique used to make overlay measurements. InFIG. 45, the indices describing the overlay measurements are:

-   -   (ico1;i″,j″;i′″,j′″)=(2;1,1;2,−2), (2;1,2;2,−1), (2;3;−2;2,1),        (2;3,−1;2,2).

A technique referred to as inter HCR/VCC adjustment is the process ofadjusting the intra VCC and intra HSR results using the inter HCR/VCCmeasurements. This technique utilizes the HV overlay measurements(BBXHV,BBYHV)(irow,ico1;i,j;i″,j″) where the indices irow,ico1,i,j,i″,j″are as defined above. In FIG. 45, the HV overlaymeasurement indices take on the values(irow,ico1;i,j;i″,j″)=(10,2,3,2,1,−2), (9,2,3,2,1,−1), (8,2,3,2,1,0),(7,2,3,2,1,1), (6,2,3,2,1,2), (5,2,3,2,3,−2), (4,2,3,2,3,

−1), (3,2,3,2,3,0), (2,2,3,2,3,1), (1,2,3,2,3,2).

Using the overlay measurements, a dynamic intra-field lens distortionmap is supplied (see Block 3514 of FIG. 35). The structure of dynamicintra-field lens distortion is (dxL, dyL)(x); is a function of the fieldcoordinate perpendicular to the scanning direction, i.e., x. A techniquefor determining intra-field lens distortion is described in A. Smith etal., “Method and Apparatus for Self-Referenced Dynamic Step and ScanIntra-Field Scanning Distortion”, U.S. Pat. No. 6,906,303, Sep. 20,2002, incorporated herein in its entirety. This technique provides thelens distortion to within a translation, rotation and x-scale factor.Preferably, the data is provided within a hierarchical structure asdescribed in “Method of Emulation of Lithographic Projection Tools”,supra.

To summarize, first reconstructions of all of the ISRs making up eachHCR are made so the position of each POLG within HCR is known to withina translation and rotation common to that row, irow. Next each VCC isreconstructed using only (BBXV,BBYV) overlay data. This process is verysimilar to HCR reconstruction and the net result is that each VCC columnhas a known position to within a translation and rotation unique to eachcolumn, ico1. Finally, the resulting unknown translations and rotationsare solved for by combining VCC and HCR reconstructions with (BBXHV,BBYHV) data. All positions are then known (to within ambiguities) andthe wafer stage grid and yaw error may be determined.

A model for the combined scan synchronization and wafer stage grid andyaw error for each independent scan row is:(Dx1,Dy1)(irow;i,j)=(tx1(irow,i),ty1(irow,i)+q1(irow,i)*xf(irow;i,j))  Equation35where:

-   -   (tx1(irow,i), ty1(irow,i)) combined wafer stage and scan        synchronization error for row irow, column i    -   q1(irow,i)=combined wafer stage and scan synchronization yaw        error    -   xf(irow;i,j)=nominal position of overlay mark with respect to        center of independent scan row.

The HCR overlay data can then be written as: $\begin{matrix}{{\left( {{BBXH},{BBYH}} \right)\left( {{{irow};1},{j;i^{\prime}},j^{\prime}} \right)} = {{s\left( {{{irow};i},{j;i^{\prime}},j^{\prime}} \right)}*\left\lbrack {{\left( {{Dx1},{Dy1}} \right)\left( {{{irow};i},j} \right)} - {\left( {{Dx1},{Dy1}} \right)\left( {{{irow};i^{\prime}},j^{\prime}} \right)} + {\left( {{dxL},{dyL}} \right)\left( {{xf}\left( {{{irow};i},j} \right)} \right)} - {\left( {{dxL},{dyL}} \right)\left( {{xf}\left( {{{irow};i^{\prime}},j^{\prime}} \right)} \right)} + {\left( {{dxR},{dyR}} \right)\left( {{{xf}\left( {{irow};{i.j.}} \right)}{{yf}\left( {{{irow};i},j} \right)}} \right)} - {\left( {{dxR},{dyR}} \right)\left( {{{xf}\left( {{{irow};i^{\prime}},j} \right)},{{yf}\left( \left( {{{irow};i^{\prime}},j^{\prime}} \right) \right)}} \right\rbrack}} \right.}} & {{Equation}\quad 36}\end{matrix}$where:

-   -   (xf,yf)(irow;i,j)=nominal y position of overlay mark with        respect to center of projected field on the wafer;    -   (dxR,dyR)(xf,yf)=overlay reticle errors expressed as equivalent        offsets at wafer (that is measured reticle error was divided        by M) at position within projected field xf, yf; and    -   s(irow;i,j;i′,j)=+1/−1 depending on whether (irow;i,j) is an        inner box (+1) or outer box (−1), this is of course known from        the exposure setup.

Because the sign factor, s, dynamic intra-field lens distortion,(dxL,dyL), and (possibly) reticle error (dxR,dyR) are known, theireffect can be removed from Equation 36 by suitable multiplication andsubtraction to the measured (BBXH,BBYH) data and we would then get:(BBXHr,BBYHr)(irow;i,j;i′,j′)=(Dx1,Dy1)(irow;i,j)−(Dx1,Dy1)(irow;i′,j′)  Equation37where:

-   -   (BBXHr,BBYHr)(irow;i,j;i′,j)=transformed (BBXH,BBYH) data.

In the foregoing, this correction is performed on the measured overlaydata, so having detailed it, it is assumed to have been done andtherefore the r suffix in Equation 37 is dropped to get:(BBXH,BBYH)(irow;i,j;i′,j′)=(Dx1,Dy1)(irow;i,j)−(Dx1,Dy1)(irow;i′,j′)  Equation38where it is understood that the overlay data has been corrected for thesign convention, intra field lens distortion, and (if the data isavailable) reticle distortion.

Using Equation 35, within HCR row number irow, the ISR translations androtations are determined by solving the equations:(BBXH,BBYHX)(irow;i,j;i′,j′)=(tx1(irow,i)−tx1(irow,i′)),ty1(irow,i)−ty1(irow,i′)+q1(irow,i)*xf(irow;i,j)−q1(irow,i′)*xf(irow;i′,j′)  Equation39Because there are at least two interlocking printed overlay groups inthe HCT exposures Equation 39 can be uniquely solved to within a commontranslation and rotation. That is, (tx1,ty1,q1) are known to within acommon translation and rotation i.e., if: (tx1(irow,i), ty1 (irow,i),q1(irow,i))=one specific solution to Equation 39 Equation 40 then we canadd to Equation 40 what corresponds geometrically to a translation andnet rotation of the row that is a gross translation (constant tx, ty)and a rotation (constant q, ty varies with i only). We denote thisambiguity by:(Tx1,Ty1,Q1)(irow)  Equation 41and uniquely specify our solution (Equation 40) of Equation 41 as havingthese three parameters set equal to zero.

To summarize, at this point the positions of each feature in each HCR isknown to within a translation and rotation that depends only on the rownumber (Equation 41).

The steps for VCC reconstruction are similar to those for HCRreconstruction except that now we are stitching together a column thatconsists of a number of independent scan rows (rotate FIG. 43 or 45 by90°). The error of independent scan rows can be modeled as:(Dx2,Dy2)(ico1;i,j)=(tx2(ico1,i)−q2(ico1,i)*yf2(ico1;i,j),ty2(ico1,i))  Equation 42where;

-   -   (tx2(ico1,i), ty2(ico1,i))=combined wafer stage and scan        synchronization error for VCC column ico1, row i;    -   q2(ico1,i)=combined wafer stage and scan synchronization yaw        error; and

(xf2,yf2)(ico1;i,j)=nominal position of overlay mark with respect tocenter of projected field on the wafer.

In all this, the coordinates are with respect to a notch down or samewafer notch angle used in the exposures described in Block 3506 in FIG.35. We reduce the box-in-box as in the HCR case (vide supra) and foreach VCC we get the set of equations (analog of Equation 33 above):(BBXV,BBYV)(ico1;i″,j″,i′″,j′″)=(tx2(ico1,i′″)−tx2(ico1,i′″))−q2(ico1,i″)*yf2(ico1;i″,j″)+q2(ico1,i′″)*yf2(ico1;i′″,j′″),ty2(ico1,i″)−ty2(ico1,i′″)  Equation 43

Again, because there are at least two interlocking POLG in between eachISR, Equation 37 an be solved for each value of ico1 uniquely to withina term that represents the net translation and rotation of the entirecolumn. This ambiguity is denoted by:(Tx2,Ty2,Q2)(ico1)  Equation 44and uniquely specify our solution (Equation 42) of Equation 43 as havingthese three parameters set equal to zero.

At this point, the unknowns in the determination are represented by theunknown translations and rotations of each HCR (Equation 41) or VCC(Equation 44). The (BBXHV, BBYHV) data can be used to stitch this datatogether. First, the HV data is reduced to remove sign conventions,intra field lens distortion and, if available, overlay reticlemanufacturing error (vide supra). Next, and referring to FIG. 45, thestitch together equations are: $\begin{matrix}{{({BBXHV})\left( {{irow},{{icol};i},{j;i^{''}},j^{''}} \right)} = {\left\lbrack {\left( {{{Tx}\quad 1({irow})} - {{Tx}\quad 2({icol})}} \right) - {Q\quad 1({irow})*\left( {{{YW}\quad 1\left( {{irow},i,j} \right)} - {{YWC}\quad 1({irow})}} \right)} + {Q\quad 2({icol})*\left( {{{YW}\quad 2\left( {{icol},i^{''},j^{''}} \right)} - {{YWC}\quad 2({icol})}} \right)}} \right\rbrack + \left\{ {{{tx}\quad 1\left( {{irow},i} \right)} - {{tx}\quad 2\left( {{icol},i^{''},j^{''}} \right)} - {q\quad 1\left( {{irow},i} \right)*{{yf}\left( {{irow},i,j} \right)}} + {q\quad 2\left( {{icol},i^{''}} \right)*{yf}\quad 2\left( {{icol},i^{''},j^{''}} \right)}} \right\}}} & {{Equation}\quad 45} \\{{({BBYHV})\left( {{irow},{{icol};i},{j;i^{''}},j^{''}} \right)} = {\left\lbrack {\left( {{{Ty}\quad 1({irow})} - {{Txy2}({icol})}} \right) - {Q\quad 1({irow})*\left( {{{XW}\quad 1\left( {{irow},i,j} \right)} - {{XWC}\quad 1({irow})}} \right)} - {Q\quad 2({icol})*\left( {{{XW}\quad 2\left( {{icol},i^{''},j^{''}} \right)} - {{XWC}\quad 2({icol})}} \right)}} \right\rbrack + \left\{ {{{ty}\quad 1\left( {{irow},i} \right)} - {{ty}\quad 2\left( {{icol},i^{''},j^{''}} \right)} + {q\quad 1\left( {{irow},i} \right)*{{xf}\left( {{irow},i,j} \right)}} - {q\quad 2\left( {{icol},i^{''}} \right)*{xf}\quad 2\left( {{icol},i^{''},j^{''}} \right)}} \right\}}} & {{Equation}\quad 46}\end{matrix}$where the new symbols mean:

-   -   (XW1,YW1)(irow,i,j)=nominal position on wafer of printed field        overlay group (Block 3506 exposure in FIG. 35) in row irow, ISR        i, transverse overlay group offset j;    -   (XW2,YW2)(ico1,i″,j″)=nominal position on wafer of printed VCC        overlay group (Block 3510 in FIG. 35 exposure) in column ico1,        ISR i″, transverse overlay group offset j″; and    -   (XWC 1,YWC 1)(irow)=nominal position on wafer of center of HCR        at row=irow    -   (XWC2,YWC2)(ico1)=nominal position on wafer of center of VCC at        column=ico1.

Quantities that are in parentheses are known from above so the onlyunknowns in Equations 39 and 40 are Tx1, Ty1, Q1, Tx2, Ty2, Q2.Equations 39 and 40 can be solved by least squares or singular valuedecomposition techniques and the only ambiguity corresponds to threevariables that geometrically corresponds to a global translation androtation of the wafer. Therefore, when we solve Equations 39 and 40 wecan uniquely specify the solution by removing global translation androtation from the resulting solution.

Alternative Solution Technique

In the above, Equations 38, 43, 45, and 46 were solved in threesuccessive steps. Another technique is to simultaneously solve for tx1,ty1, q1, tx2, ty2, q2 using Equations 39 and 43 above along with thestitching equations:(BBXHV)(irow,ico1;i,j;i″,j″)={tx1(irow,i)−tx2(ico1,i″,j″)−q1(irow,i)*yf(irow,i,j)+q2(ico1,i′)*yf2(ico1,i″,j″)}  Equation47(BBYHV)(irow,ico1;i,j;i″,j″)={ty1(irow,i)−ty2(ico1,i″,j″)+q1(irow,i)*xf(irow,i,j)−q2(ico1,i″)*xf2(ico1,i″,j″)}  Equation48where (BBXHV, BBYHV) are the reduced overlay measurements (vide supra).Including the stitching Equations 47 and 48 and solving simultaneouslyalong with Equations 39 and 43 reduces the ambiguity in the finalsolution to three parameters that correspond to a global translation (xand y) and rotation of the wafer. So, if we have any simultaneoussolution to Equations 39, 43, 47 and 48 and then remove the globaltranslation and rotation, we have a unique solution.Wafer Stage Grid and Yaw

At this point the quantities (tx1, ty1, q1) (irow,i) are known. Itremains to provide an expression for wafer stage grid (TXWS(IP),TYWS(IP)) and yaw (QWS(IP)). We have directly;TXWS(IP)=sum{irow,iε PF(IP)|tx1(irow,i)}/N(irow,i)  Equation 49TYWS(IP)=sum{irow, iε PF(IP)|ty1(irow,i)}/N(irow,i)  Equation 50QWS(IP)=sum{irow, iε PF(IP)|q1(irow,i)}/N(irow,i)  Equation 51N(irow,i)=sum{irow,iε PF(IP)|1}  Equation 52Where:

-   ‘irow, iε PF(IP)’ means only ISRs that are contained in printed    field number IP contribute to the sum.

So, N(irow,I)=number of ISRs that make up printed field number IP.Equations 49, 50 and 51 allow us to produce the stage grid and yawerror. FIG. 46 is a table illustrating an exemplary output listing ofstage grid and yaw errors for a scanner operating in dynamic mode.

Alternative Embodiments

The terms (tx1, ty1, q1) (irow,i) (vide supra) also contain the dynamicscan synchronization error for each production field scan (see Equation53 below). The system can also report these as additional outputs towafer stage grid and yaw.tx1(irow,i)−TXWS(IP);ty1(irow,i)−TYWS(IP);q1(irow,i)−QWS(IP)  Equation53

Other Embodiments and Variations

FIG. 47 is a block diagram of an example of a projection imaging tool(PIT). As shown in FIG. 47, the projection imaging tool includes aneffective source ES, a reticle stage RS, projection imaging optics PIO,and a wafer stage WS. The effective source ES includes a light sourceLS, input illuminator optics IIO and output illumination optics OIO.

The reticle stage RS holds a pellicle PE reticle(R) combination. Forexample, the reticle stage may be used to hold, and position, reticlesconfigured as described in the above embodiments.

The projection imaging optics include input projection optics, anaperture stop, and output projection optics. The wafer stage WS isconfigured to hold and position a photo resist coated wafer.

The operation of the projection imaging system can be adjusted inresponse to the reconstructed wafer grid and yaw error. For example, acontroller in the projection imaging system can adjust the operation ofthe wafer stage response to the reconstructed wafer grid and yaw error.The positioning of the reticle relative to the substrate can beaccomplished by a translation stage such as a wafer stage or a reticlestage of both. Likewise the substrate can be rotated relative to thewafer by a rotational stage, such as a wafer stage, reticle stage orboth.

The techniques can be used to improve semiconductor fabrication thatuses a photolithographic projection tool. For example, operation of theprojection imaging system can be adjusted in response to thereconstructed wafer grid and yaw error to improve throughput, or yield,in a semiconductor fabrication process.

Heretofore, it has been considered the reticle creating the overlaypatterns as perfect. In practice it is not, but errors in the reticlemanufacture can be taken into account by first measuring the position ofall the individual structures in all of the overlay groups using anabsolute metrology tool such as the Nikon 5I (See Measuring SystemXY-5i, supra), or Leica LMS 3200 series tools. Next, in formulatingEquations 20-23, this reticle error (divided by the photolithographicexposure tool demagnification) is explicitly written out on the righthand side and then subtracted from the resulting overlay measurements onthe left hand side of the equations (thereby canceling out on the righthand side). The result is Equations 20-23 as they are written above butwith a correction applied to the overlay measurements appearing on theleft hand side. The analysis then proceeds word for word as before.

The reticle of the present invention is typically glass or fused silicawith openings defined in a chrome coating. This is common for projectionlithography tools utilized in semiconductor manufacture. The form thereticle can take will be determined by the format required by thespecific projection imaging tool on which the reticle is loaded. Thusfor purposes of analyzing copying machine performance, the reticle OL ofthe present invention would consist of a piece of paper or mylar withoverlay groups disposed on it. In an extreme ultra violet (EUV) exposuretool the mask would be reflective.

The completed alignment attributes of the present invention so fardiscussed are of the box in box, bar in bar, or wafer alignment marksmost commonly used in semiconductor manufacture. In practice, hundredsof different overlay target patterns are available (See Handbook ofMicrolithography and Microfabrication, supra; Direct-ReferencingAutomatic Two-Points Reticle-to-Wafer Alignment Using a ProjectionColumn Servo System, M. Van den Brink et al., SPIE Vol. 633, OpticalMicrolithography V, 60:71, 1986; Overlay Alignment Measurement ofWafers, N. Bareket, U.S. Pat. No. 6,079,256, Jun. 27, 2000; FIG. 1 b),some common completed alignment attributes are shown in FIG. 3. Theexact form taken by the completed alignment attributes will bedetermined by the overlay metrology used in the measurement step.

The overlay metrology tool utilized by the present invention istypically a conventional optical overlay tool such as those manufacturedby KLA-Tencor (See KLA 5105 Overlay Brochure, supra; KLA 5200 OverlayBrochure, KLA-Tencor) or Bio-Rad Semiconductor Systems. See Quaestor Q7Brochure, Bio-rad Semiconductor Systems. Other optical overlay toolsthat can be used by the present invention include those described in SeeProcess for Measuring Overlay Misregistration During Semiconductor WaferFabrication, I. Mazor et al., U.S. Pat. No. 5,438,413, Aug. 1, 1995. Inaddition, some steppers or scanners (See Matching Management of MultipleWafer Steppers Using a Stable Standard and a Matching Simulator, supra)can utilize their wafer alignment systems and wafer stages to functionas overlay tools. However, in this role we would limit the total size ofthe alignment attribute (consisting of two wafer alignment marks) to adistance over which the wafer stage would be as accurate as aconventional optical overlay tool. This distance is typically less thanabout 2.0 mm. When electrical alignment attributes are used for overlay(See Matching Mariagement of Multiple Wafer Steppers Using a StableStandard and a Matching Simulator, supra; Automated ElectricalMeasurements of Registration Errors in Step and Repeat OpticalLithography Systems, T. Hasan et al., IEEE Transaction on ElectronDevices, Vol. ED-27, No. 12, 2304:2312, December 1980; Capacitor CircuitStructure for Determining Overlay Error, K. Tzeng et al., U.S. Pat. No.6,143,621, Nov. 7, 2000), the overlay metrology tool as utilized by thisinvention would correspond to the electrical equipment utilized formaking the corresponding measurement.

The present invention has been mainly described with respect to itsapplication on the projection imaging tools (scanners (See Micrascan™III Performance of a Third Generation, Catadioptric Step and ScanLithographic Tool, D. Cote et al., SPIE Vol. 3051, 806:816, 1997; ArFStep and Scan Exposure System for 0.15 Micron and 0.13 Micron TechnologyNode, J. Mulkens et al., SPIE Conference on Optical MicrolithographyXII, 506:521, March 1999; 0.7 NA DUV Step and Scan System for 150 nmImaging with Improved Overlay, J. V. Schoot, SPIE Vol. 3679, 448:463,1999) commonly used in semiconductor manufacturing today. The methods ofthe present invention can be applied to other scanning projection toolssuch as; 2-dimensional scanners (See Large-Area, High-Throughput, HighResolution Projection Imaging System, Jain, U.S. Pat. No. 5,285,236,Feb. 8, 1994; Optical Lithography—Thirty Years and Three Orders ofMagnitude, supra), office copy machines, and next generation lithography(ngl) systems such as XUV (See Development of XUV Projection Lithographyat 60-80 nm, B. Newnam et al., SPIE Vol. 1671, 419:436, 1992), SCALPEL,EUV (Extreme Ultra Violet) (See Reduction Imaging at 14 nm UsingMultilayer-Coated Optics: Printing of Features Smaller than 0.1 Micron,J. Bjorkholm et al., Journal Vacuum Science and Technology, B 8(6),1509:1513, November/December 1990), IPL (Ion Projection Lithography),and EPL (electron projection lithography). See Mix-and Match: ANecessary Choice, supra.

The present invention has been mainly described with respect to therecording medium being positive photoresist. The present invention couldequally well have used negative photoresist providing we makeappropriate adjustment to the overlay groups on the reticle. In general,the recording medium is whatever is typically used on the lithographicprojection tool we are measuring. Thus, on an EPL tool, an electron beamphotoresist such as PMMA could be utilized as the recording medium.

So far, we have described the substrates on which the recording media isplaced as wafers. This will be the case in semiconductor manufacture.The exact form of the substrate will be dictated by the projectionlithography tool and its use in a specific manufacturing environment.Thus, in a flat panel manufacturing facility, the substrate on which thephotoresist would be placed would be a glass plate or panel. A maskmaking tool would utilize a reticle as a substrate. Circuit boards ormulti-chip module carriers are other possible substrates.

The foregoing description details certain embodiments of the invention.It will be appreciated, however, that no matter how detailed theforegoing appears, the invention may be embodied in other specific formswithout departing from its spirit or essential characteristics. Thedescribed embodiments are to be considered in all respects only asillustrative and not restrictive and the scope of the invention is,therefore, indicated by the appended claims rather than by the foregoingdescription. All changes, which come with the meaning and range ofequivalency of the claims, are to be embraced within their scope.

1. A method of determining wafer stage grid and yaw in a projectionimaging tool, the method comprising: exposing an overlay reticle in atleast three positions onto a substrate having a recording media, therebycreating a plurality of printed fields; positioning the overlay reticlesuch that, when the reticle is exposed, completed alignment attributesare created in at least two sites comprising a first printed field and asecond printed field; rotating the substrate a desired amount;positioning the overlay reticle such that, when the reticle is exposed,completed alignment attributes are created in at least two sitescomprising the first printed field and third printed field; andreconstructing wafer stage grid and yaw error of the projection imagingsystem from measurements of the completed complementary alignmentattributes and a dynamic intra-field lens distortion.
 2. A method asdefined in claim 1, wherein rotating the substrate a desired amountcomprises rotating 90 degrees.
 3. A method as defined in claim 1,wherein measurements of the complementary alignment attribute are madewith an overlay metrology tool.
 4. A method as defined in claim 1,wherein the substrate is a semiconductor wafer, a flat panel display, areticle, or an electronic recording media.
 5. A method as defined inclaim 1, wherein the projection imaging tool is a photolithograph stepand scan machine, a photolithographic scanner machine, a scanningelectron beam imaging system, a scanning direct write tool, a scalpeltool, a scanning extreme ultra-violet photolithographic tool, or ascanning x-ray imaging system.
 6. A method as defined in claim 1,wherein the recording media is a positive photoresist material, anegative photoresist material, an electronic CCD, a diode array, aliquid crystal, or an optically sensitive material.
 7. A method asdefined in claim 1, further comprising adjusting operation of theprojection imaging tool in response to the reconstructed wafer grid andyaw error.
 8. A method of determining wafer stage grid and yaw in aprojection imaging tool, the method comprising: exposing an overlayreticle in at least four positions onto a substrate having a recordingmedia, thereby creating a plurality of printed fields; positioning theoverlay reticle such that, when the reticle is exposed, completedalignment attributes are created in at least two sites comprising afirst printed field and a second printed field; positioning the overlayreticle such that, when the reticle is exposed, completed alignmentattributes are created in at least two sites comprising a third printedfield and a fourth printed field; rotating the substrate 90 degrees;positioning the overlay reticle such that, when the reticle is exposed,completed alignment attributes are created in at least two sitescomprising the first printed field and the third printed field;positioning the overlay reticle such that, when the reticle is exposed,completed alignment attributes are created in at least two sitescomprising the second printed field and the fourth printed field; andreconstructing wafer stage grid and yaw error of the projection imagingsystem from measurements of the complementary alignment attribute and adynamic intra-field lens distortion.
 9. A method as defined in claim 8,wherein measurements of the complementary alignment attribute are madewith an overlay metrology tool.
 10. A method as defined in claim 8,wherein the substrate is a semiconductor wafer, a flat panel display, areticle, or an electronic recording media.
 11. A method as defined inclaim 8, wherein the projection imaging tool is a photolithograph stepand scan machine, a photolithographic scanner machine, a scanningelectron beam imaging system, a scanning direct write tool, a scalpeltool, a scanning extreme ultra-violet photolithographic tool, or ascanning x-ray imaging system.
 12. A method as defined in claim 8,wherein the recording media is a positive photoresist material, anegative photoresist material, an electronic CCD, a diode array, aliquid crystal, or an optically sensitive material.
 13. A method asdefined in claim 8, further comprising adjusting operation of theprojection imaging tool in response to the reconstructed wafer grid andyaw error.
 14. A projection imaging system comprising an overlay reticlethat is exposed in at least three positions onto a substrate having arecording media, thereby creating a plurality of printed fields; atranslation stage that positions the overlay reticle relative to thesubstrate such that when the reticle is exposed completed alignmentattributes are created in at least two sites in a first and a secondprinted field; a rotation stage that rotates the substrate a desiredamount, wherein the translational stage positions the overlay reticlerelative to the substrate such that when the reticle is exposedcompleted alignment attributes are created in at least two sites in afirst and third printed field; and a controller configured to adjust theoperation of the projection imaging system in response to areconstructed wafer stage grid and yaw error of the projection imagingsystem determined from measurements of the complementary alignmentattribute and a dynamic intra-field lens distortion.
 15. A projectionimaging system as defined in claim 14, wherein the translation stagecomprises a wafer stage.
 16. A projection imaging system as defined inclaim 14, wherein the translation stage comprises a reticle stage.
 17. Aprojection imaging system as defined in claim 14, wherein the rotationalstage comprises a wafer stage.
 18. A projection imaging system asdefined in claim 14, wherein the rotational stage comprises a reticlestage.
 19. A projection imaging system as defined in claim 14, whereinthe translation stage and rotational stage are the same.
 20. Aprojection imaging tool comprising: means for exposing an overlayreticle in at least three positions onto a substrate having a recordingmedia, thereby creating a plurality of printed fields; means forpositioning the overlay reticle such that when the reticle is exposedcompleted alignment attributes are created in at least two sites in afirst and a second printed field; means for rotating the substrate adesired amount; means for positioning the overlay reticle such that whenthe reticle is exposed completed alignment attributes are created in atleast two sites in a first and third printed field; and means forreconstructing wafer stage grid and yaw error of the projection imagingsystem from measurements of the complementary alignment attribute and adynamic intra-field lens distortion.
 21. A projection imaging system asdefined in claim 20, further comprising means for adjusting theoperation of the projection imaging system in response to thereconstructed wafer stage grid and yaw error.
 22. A projection imagingtool comprising: means exposing an overlay reticle in at least fourpositions onto a substrate having a recording media, thereby creating aplurality of printed fields; means for positioning the overlay reticlesuch that when the reticle is exposed completed alignment attributes arecreated in at least two sites in a first and a second printed field;means for positioning the overlay reticle such that when the reticle isexposed completed alignment attributes are created in at least two sitesin a third and a fourth printed field; means for rotating the substrate90 degrees; means for positioning the overlay reticle such that when thereticle is exposed completed alignment attributes are created in atleast two sites in the first and third printed field; means forpositioning the overlay reticle such that when the reticle is exposedcompleted alignment attributes are created in at least two sites in thesecond and fourth printed field; and means for reconstructing waferstage grid and yaw error of the projection imaging system frommeasurements of the complementary alignment attribute and a dynamicintra-field lens distortion.
 23. A projection imaging system as definedin claim 22, further comprising means for adjusting the operation of theprojection imaging system in response to the reconstructed wafer stagegrid and yaw error.